2,828 results on '"NONCONVEX programming"'
Search Results
2. Optimality conditions and sensitivity analysis in parametric nonconvex minimax programming.
- Author
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An, D. T. V., Hung, N. H., Ngoan, D. T., and Tuyen, N. V.
- Subjects
NONCONVEX programming ,SUBDIFFERENTIALS ,SENSITIVITY analysis - Abstract
In this paper, we perform optimality conditions and sensitivity analysis for parametric nonconvex minimax programming problems. Our aim is to study the necessary optimality conditions by using the Mordukhovich (limiting) subdifferential and to give upper estimations for the Mordukhovich subdifferential of the optimal value function in the problem under consideration. The optimality conditions and sensitivity analysis are obtained by using upper estimates for Mordukhovich subdifferentials of the maximum function. The results on optimality conditions are then applied to parametric multiobjective optimization problems. An example is given to illustrate our results. [ABSTRACT FROM AUTHOR]
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- 2024
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3. Solving Two-Trust-Region Subproblems Using Semidefinite Optimization with Eigenvector Branching.
- Author
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Anstreicher, Kurt M.
- Subjects
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SEMIDEFINITE programming , *NONCONVEX programming , *EIGENVECTORS , *QUADRATIC programming , *MATHEMATICS - Abstract
Semidefinite programming (SDP) problems typically utilize a constraint of the form X ⪰ x x T to obtain a convex relaxation of the condition X = x x T , where x ∈ R n . In this paper, we consider a new hyperplane branching method for SDP based on using an eigenvector of X - x x T . This branching technique is related to previous work of Saxeena et al. (Math Prog Ser B 124:383–411, 2010, https://doi.org/10.1007/s10107-010-0371-9) who used such an eigenvector to derive a disjunctive cut. We obtain excellent computational results applying the new branching technique to difficult instances of the two-trust-region subproblem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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4. A Generalized Formulation for Group Selection via ADMM.
- Author
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Ke, Chengyu, Shin, Sunyoung, Lou, Yifei, and Ahn, Miju
- Abstract
This paper studies a statistical learning model where the model coefficients have a pre-determined non-overlapping group sparsity structure. We consider a combination of a loss function and a regularizer to recover the desired group sparsity patterns, which can embrace many existing works. We analyze directional stationary solutions of the proposed formulation, obtaining a sufficient condition for a directional stationary solution to achieve optimality and establishing a bound of the distance from the solution to a reference point. We develop an efficient algorithm that adopts an alternating direction method of multiplier (ADMM), showing that the iterates converge to a directional stationary solution under certain conditions. In the numerical experiment, we implement the algorithm for generalized linear models with convex and nonconvex group regularizers to evaluate the model performance on various data types, noise levels, and sparsity settings. [ABSTRACT FROM AUTHOR]
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- 2024
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5. A new proximal heavy ball inexact line-search algorithm.
- Author
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Bonettini, S., Prato, M., and Rebegoldi, S.
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ALGORITHMS ,TABU search algorithm ,NONCONVEX programming - Abstract
We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variable metric proximal-gradient iteration with momentum and an Armijo-like linesearch based on the sufficient decrease of a suitable merit function. The linesearch procedure allows for a major flexibility on the choice of the algorithm parameters. We prove the convergence of the iterates sequence towards a stationary point of the problem, in a Kurdyka–Łojasiewicz framework. Numerical experiments on a variety of convex and nonconvex problems highlight the superiority of our proposal with respect to several standard methods, especially when the inertial parameter is selected by mimicking the Conjugate Gradient updating rule. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Revenue maximization based joint optimization in mmWave cell-free network: an equivalent decomposition and alternative iteration combined approach.
- Author
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Ma, Zhongyu, Ran, Liang, Pu, Jianbing, Guo, Qun, and Lin, Xianghong
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INTERIOR-point methods ,NONCONVEX programming ,POLYNOMIAL time algorithms ,NP-hard problems ,POWER transmission ,COMPUTATIONAL complexity - Abstract
Recently, the ever-increasing demands including higher rate and connection stability have bottlenecked the user experience of the traditional cellular networks. To this end, the Cell-Free (CF) network, which is characterized as a user-centric architecture, is viewed as a promising paradigm to enhance the user experience. Aimed at this point, this paper investigates the joint optimization problem including user matching, sub-channel allocation and power controlling for the mmWave CF network to maximize the revenue of the operators. Firstly, the revenue maximization oriented joint optimization problem of the mmWave CF network is formulated as mixed integer non-convex and non-linear programming, which is NP-hard problem and is intractable to search an optimal solution in within polynomial time. Secondly, the original problem is decomposed into three sub-problems, i.e., user association sub-problem, the sub-channel allocation sub-problem and the power controlling sub-problem under the consideration of the matching quotas, rate demand and transmission power, etc. Thirdly, a many-to-many matching based user association algorithm and an alternating iterative joint resource management algorithm, which is composed of the harmony search based sub-channel allocation sub-algorithm and the interior-point method based power controlling sub-algorithm, are proposed to obtain a sub-optimal solution, and the computational complexity of the proposed algorithms are also analyzed. Finally, the performance superiorities of the proposed algorithms are demonstrated through extensive simulations, and it is demonstrated that the proposed algorithms can outperform the proposed algorithm outperforms the PUAA algorithm by 5.73% and the SRAA algorithm by 11.25% in terms of operator revenue. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Self-adaptive algorithms for quasiconvex programming and applications to machine learning.
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Thang, Tran Ngoc and Hai, Trinh Ngoc
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MACHINE learning ,NONCONVEX programming ,ALGORITHMS ,FEATURE selection ,SELF-adaptive software ,CONSTRAINT programming ,LOGISTIC regression analysis - Abstract
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach under mild assumptions. Specifically, the objective function may not satisfy the convexity condition. Unlike descent line-search algorithms, it does not need a known Lipschitz constant to figure out how big the first step should be. The crucial feature of this process is the steady reduction of the step size until a certain condition is fulfilled. In particular, it can provide a new gradient projection approach to optimization problems with an unbounded constrained set. To demonstrate the effectiveness of the proposed technique for large-scale problems, we apply it to some experiments on machine learning, such as supervised feature selection, multi-variable logistic regressions and neural networks for classification. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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8. The Nonconvex Second-Order Cone: Algebraic Structure Toward Optimization.
- Author
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Alzalg, Baha and Benakkouche, Lilia
- Subjects
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JORDAN algebras , *NONCONVEX programming , *QUADRATIC programming , *QUADRATIC forms , *ALGEBRA , *CONVEX bodies - Abstract
This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as a higher-dimensional conic extension of the known causality cone in relativity. The nonconvex second-order cone can be used to reformulate nonconvex quadratic programming and nonconvex quadratically constrained quadratic program in conic format. The cone can also arise in real-world applications, such as facility location problems in optimization when some existing facilities are more likely to be closer to new facilities than other existing facilities. We define notions of the algebraic structure of the nonconvex second-order cone and show that its ambient space is commutative and power-associative, wherein elements always have real eigenvalues; this is remarkable because it is not the case for arbitrary Jordan algebras. We will also find that the ambient space of this nonconvex cone is rank-independent of its dimension; this is also notable because it is not the case for algebras of arbitrary convex cones. What is more noteworthy is that we prove that the nonconvex second-order cone equals the cone of squares of its ambient space; this is not the case for all non-Euclidean Jordan algebras. Finally, numerous algebraic properties that already exist in the framework of the convex second-order cone are generalized to the framework of the nonconvex second-order cone. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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9. An MTL1TV non-convex regularization model for MR Image reconstruction using the alternating direction method of multipliers.
- Author
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You, Xuexiao, Cao, Ning, and Wang, Wei
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MULTIPLIERS (Mathematical analysis) , *IMAGE reconstruction , *NONCONVEX programming , *NUMERICAL analysis , *MATHEMATICAL models - Abstract
The acquisition time of magnetic resonance imaging (MRI) is relatively long. To achieve high-quality and fast reconstruction of magnetic resonance (MR) images, we proposed a non-convex regularization model for MR image reconstruction with the modified transformed l 1 total variation (MTL1TV) regularization term. We addressed this new model using the alternating direction method of multipliers (ADMM). To evaluate the proposed MTL1TV model, we performed numerical experiments on several MR images. The numerical results showed that the proposed model gives reconstructed images of improved quality compared with those obtained from state of the art models. The results indicated that the proposed model can effectively reconstruct MR images. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. On optimization of lightweight planar frame structures: an evolving ground structure approach.
- Author
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Toragay, Oguz, Silva, Daniel F., and Vinel, Alexander
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STRUCTURAL frames , *NONCONVEX programming , *MATHEMATICAL programming , *INTEGER programming , *HEURISTIC - Abstract
We consider the problem of designing lightweight, load-bearing planar frame structures for additive manufacturing, which can be formulated as a nonlinear, non-convex mathematical programming problems. Even using state-of-the-art commercial solvers, exact methods are only capable of solving small unrealistic instances (with very few variables). In this paper, we develop a heuristic method which is fast and capable of solving the design problem for larger-scale, weight-optimized, planar frame structures for additive manufacturing. The approach explicitly considers manufacturability constraints stemming from the use of additive manufacturing technology and leverages the problem structure imposed by these constraints. The proposed heuristic method is based on iteratively resolving a relaxed master problem on a reduced ground structure. The approach differs from the existing methods in two important aspects. First, we consider planar frame optimization master problem directly (instead of simpler but less relevant truss optimization). Secondly, we employ both element and node addition, which allows us to enforce additive manufacturability constraints without using binary variables (and hence, avoiding the need for computationally expensive integer programming). [ABSTRACT FROM AUTHOR]
- Published
- 2024
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11. OPTIMALITY CONDITIONS FOR NONCONVEX MATHEMATICAL PROGRAMMING PROBLEMS USING WEAK SUBDIFFERENTIALS AND AUGMENTED NORMAL CONES.
- Author
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TRAN VAN SU and CHU VAN TIEP
- Subjects
NONCONVEX programming ,SUBDIFFERENTIALS ,CONVEX functions ,MATHEMATICAL programming ,VECTOR algebra - Abstract
In this paper, we study some characterizations of the class of weakly subdifferentiable functions and formulate optimality conditions for nonconvex mathematical programming problems described by the class of weakly subdifferentiable functions in real normed spaces. The necessary and sufficient optimality conditions for a nonconvex scalar function with a global minimum/or a global maximum at a given vector via the weak subdifferentials and augmented normal cones are established. Additionally, the necessary and sufficient optimality conditions for a nonconvex vector function with a weakly efficient solution/or an efficient solution at a given vector via the augmented weak subdifferentials and normal cones are presented too. Finally, our optimality conditions are used to derive the necessary optimality conditions for nonsmooth nonconvex mathematical programming problems with set, inequality, and equality constraints. [ABSTRACT FROM AUTHOR]
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- 2024
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12. A PARAMETERIZED THREE-OPERATOR SPLITTING ALGORITHM FOR NON-CONVEX MINIMIZATION PROBLEMS WITH APPLICATIONS.
- Author
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LIUYI MIAO, YUCHAO TANG, and CHANGLONG WANG
- Subjects
PARAMETERIZATION ,STOCHASTIC convergence ,LIPSCHITZ spaces ,NONCONVEX programming ,MATHEMATICAL regularization - Abstract
In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients. We establish the convergence of the proposed algorithm under the KurdykaŁojasiewicz assumption by constructing a suitable energy function with a non-increasing property. As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems. Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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13. A non-linear convex model based energy management strategy for dual-storage offshore wind system.
- Author
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Tian, Tian, Ma, Zetao, Shu, Jie, Cui, Qiong, Bie, Kang, Tang, Lei, and Wang, Hao
- Subjects
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BATTERY storage plants , *ENERGY management , *NONCONVEX programming , *DYNAMIC programming , *HYDROGEN as fuel , *POWER resources , *CONVEX programming - Abstract
—Using hydrogen production as energy storage can realize large-scale storage and transportation of energy, which is conducive to flexible scheduling of offshore wind power resources. However, compared with the battery energy storage system, the energy management strategy (EMS) of the dual-storage offshore wind power system with hydrogen production is more complex and nonlinear due to the large number of state variables and control variables. In order to realize the EMS of the system to maximize the benefits and minimize the aging cost, a nonlinear convex model is first established, and then an iterative solution method combining convex programming (CP) and dynamic programming (DP) is proposed. Among them, CP solves the global optimization problem of power distribution, and DP determines the start and stop of the electrolyzer. Finally, the feasibility of the proposed method is verified by simulation analysis. [Display omitted] • Conversion among different working states of the electrolyzer is considered, including cold start and warm start. • Degradation models of the electrolyzer and battery storage are considered for their state of health preservation. • An iterative algorithm combing dynamic programming and convex programming is proposed to search the optimal power splits and the electrolyzer state. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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14. Riemannian Interior Point Methods for Constrained Optimization on Manifolds.
- Author
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Lai, Zhijian and Yoshise, Akiko
- Subjects
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INTERIOR-point methods , *NONCONVEX programming , *CONSTRAINED optimization , *NONLINEAR programming - Abstract
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish its local superlinear and quadratic convergence under the standard assumptions. Moreover, we show its global convergence when it is combined with a classical line search. Our method is a generalization of the classical framework of primal-dual interior point methods for nonlinear nonconvex programming. Numerical experiments show the stability and efficiency of our method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. On a solution method in indefinite quadratic programming under linear constraints.
- Author
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Cuong, Tran Hung, Lim, Yongdo, and Yen, Nguyen Dong
- Subjects
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LINEAR programming , *QUADRATIC programming , *NONCONVEX programming , *ALGORITHMS - Abstract
We establish some properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming under linear constraints. The first property states that any iterative sequence generated by the algorithm is root linearly convergent to a Karush–Kuhn–Tucker point, provided that the problem has a solution. The second property says that iterative sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably chosen neighbourhood of it. Through a series of numerical tests, we analyse the influence of the decomposition parameter on the rate of convergence of the iterative sequences and compare the performance of the Proximal Difference-of-Convex functions decomposition algorithm with that of the Projection Difference-of-Convex functions decomposition algorithm. In addition, the performances of the above algorithms and the Gurobi software in solving some randomly generated nonconvex quadratic programs are compared. [ABSTRACT FROM AUTHOR]
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- 2024
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16. DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor.
- Author
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Li, Wan-Li, Li, Jiong, Ye, Ji-Kun, Shao, Lei, and Zhou, Chi-Jun
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REINFORCEMENT learning ,DEEP reinforcement learning ,MACHINE learning ,NONCONVEX programming ,CONVEX programming ,ALGORITHMS ,APPROXIMATION error - Abstract
To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. A global optimization approach to Berge equilibrium based on a regularized function
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Battur, G., Batbileg, S., and Enkhbat, R.
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- 2024
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18. Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming.
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Harwood, Stuart, Trespalacios, Francisco, Papageorgiou, Dimitri, and Furman, Kevin
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BILEVEL programming ,NONCONVEX programming ,NASH equilibrium ,GLOBAL optimization ,COMPLEMENTARITY constraints (Mathematics) ,EQUILIBRIUM - Abstract
Methods for finding pure Nash equilibria have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the players' decision problems, they only apply as heuristic methods when the players are modeled by nonconvex optimization problems. In contrast, this work approaches Nash equilibrium using theory and methods for the global optimization of nonconvex bilevel programs. Through this perspective, we draw precise connections between Nash equilibria, feasibility for bilevel programming, the Nikaido–Isoda function, and classic arguments involving Lagrangian duality and spatial price equilibrium. Significantly, this is all in a general setting without the assumption of convexity. Along the way, we introduce the idea of minimum disequilibrium as a solution concept that reduces to traditional equilibrium when an equilibrium exists. The connections with bilevel programming and related semi-infinite programming permit us to adapt global optimization methods for those classes of problems, such as constraint generation or cutting plane methods, to the problem of finding a minimum disequilibrium solution. We propose a specific algorithm and show that this method can find a pure Nash equilibrium even when the players are modeled by mixed-integer programs. Our computational examples include practical applications like unit commitment in electricity markets. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. Hyperspectral super-resolution via low rank tensor triple decomposition.
- Author
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Cui, Xiaofei and Chang, Jingya
- Subjects
IMAGE fusion ,OPTIMIZATION algorithms ,HIGH resolution imaging ,MULTISPECTRAL imaging ,SPECTRAL imaging ,NONCONVEX programming - Abstract
Hyperspectral image (HSI) and multispectral image (MSI) fusion aims at producing a super-resolution image (SRI). In this paper, we establish a nonconvex optimization model for image fusion problem through low rank tensor triple decomposition. Using the limited memory BFGS (L-BFGS) approach, we develop a first-order optimization algorithm for obtaining the desired super-resolution image (TTDSR). Furthermore, two detailed methods are provided for calculating the gradient of the objective function. With the aid of the Kurdyka-Łojasiewicz property, the iterative sequence is proved to converge to a stationary point. Finally, experimental results on different datasets show the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Robust Nonconvex Sparse Optimization for Impact Force Identification.
- Author
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Liu, Junjiang, Qiao, Baijie, Wang, Yanan, He, Weifeng, and Chen, Xuefeng
- Subjects
AMPLITUDE estimation ,COMPOSITE structures ,NONCONVEX programming ,COMPUTER simulation - Abstract
The inherent sparse structure of impact forces has garnered considerable attention in the field of impact force identification. However, conventional convex sparse regularization methods, including the widely used ℓ 1 regularization, often encounter challenges such as underestimation of impact amplitudes and biased estimations. To address these limitations, we propose a robust nonconvex sparse regularization method for impact force identification. The key advantage of our method is the simultaneous retention of robustness and unbiasedness. The robustness of our method is primarily achieved through an efficient solver developed within the alternating direction method of multipliers (ADMM) framework. By combining convex and nonconvex strategies, the ADMM solver separates the intractable nonconvex problem into more manageable convex sub-problems. Additionally, the ADMM solver incorporates the firm-thresholding operator, which ensures an unbiased amplitude distribution and preserves the impact amplitudes. With a sparse and under-determined sensor configuration, our proposed method enables simultaneous impact localization and time-history reconstruction. We comprehensively demonstrate the algorithmic performance through a series of numerical simulations and laboratory experiments on typical composite structures. The comparative results clearly indicate that our proposed approach achieves significant improvements in identification accuracy compared to classical sparse regularization methods, such as ℓ 1 and ℓ 0 regularization. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Open issues and recent advances in DC programming and DCA.
- Author
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Le Thi, Hoai An and Pham Dinh, Tao
- Subjects
APPLIED sciences ,NONCONVEX programming ,GLOBAL optimization ,NONSMOOTH optimization ,CONVEX functions ,RESEARCH personnel - Abstract
DC (difference of convex functions) programming and DC algorithm (DCA) are powerful tools for nonsmooth nonconvex optimization. This field was created in 1985 by Pham Dinh Tao in its preliminary state, then the intensive research of the authors of this paper has led to decisive developments since 1993, and has now become classic and increasingly popular worldwide. For 35 years from their birthday, these theoretical and algorithmic tools have been greatly enriched, thanks to a lot of their applications, by researchers and practitioners in the world, to model and solve nonconvex programs from many fields of applied sciences. This paper is devoted to key open issues, recent advances and trends in the development of these tools to meet the growing need for nonconvex programming and global optimization. We first give an outline in foundations of DC programming and DCA which permits us to highlight the philosophy of these tools, discuss key issues, formulate open problems, and bring relevant answers. After outlining key open issues that require deeper and more appropriate investigations, we will present recent advances and ongoing works in these issues. They turn around novel solution techniques in order to improve DCA's efficiency and scalability, a new generation of algorithms beyond the standard framework of DC programming and DCA for large-dimensional DC programs and DC learning with Big data, as well as for broader classes of nonconvex problems beyond DC programs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Online Joint Optimization of Virtual Network Function Deployment and Trajectory Planning for Virtualized Service Provision in Multiple-Unmanned-Aerial-Vehicle Mobile-Edge Networks.
- Author
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He, Qiao and Liang, Junbin
- Subjects
VIRTUAL networks ,DEEP reinforcement learning ,REINFORCEMENT learning ,NONCONVEX programming ,DRONE aircraft ,EDGE computing ,NP-complete problems - Abstract
The multiple-unmanned-aerial-vehicle (multi-UAV) mobile edge network is a promising networking paradigm that uses multiple resource-limited and trajectory-planned unmanned aerial vehicles (UAVs) as edge servers, upon which on-demand virtual network functions (VNFs) are deployed to provide low-delay virtualized network services for the requests of ground users (GUs), who often move randomly and have difficulty accessing the Internet. However, VNF deployment and UAV trajectory planning are both typical NP-complete problems, and the two operations have a strong coupling effect: they affect each other. Achieving optimal virtualized service provision (i.e., maximizing the number of accepted GU requests under a given period T while minimizing the energy consumption and the cost of accepting the requests in all UAVs) is a challenging issue. In this paper, we propose an improved online deep reinforcement learning (DRL) scheme to tackle this issue. First, we formulate the joint optimization of the two operations as a nonconvex mixed-integer nonlinear programming problem, which can be viewed as a sequence of one-frame joint VNF deployment and UAV-trajectory-planning optimization subproblems. Second, we propose an online DRL based on jointly optimizing discrete (VNF deployment) and continuous (UAV trajectory planning) actions to solve each subproblem, whose key idea is establishing and achieving the coupled influence of discrete and continuous actions. Finally, we evaluate the proposed scheme through extensive simulations, and the results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. GLOBAL COMPLEXITY BOUND OF A PROXIMAL ADMM FOR LINEARLY CONSTRAINED NONSEPARABLE NONCONVEX COMPOSITE PROGRAMMING.
- Author
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KONG, WEIWEI and MONTEIRO, RENATO D. C.
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NONCONVEX programming , *LAGRANGIAN functions , *LAGRANGE multiplier - Abstract
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable. Each iteration of DP.ADMM consists of (i) a sequence of partial proximal augmented Lagrangian (AL) updates, (ii) an under-relaxed Lagrange multiplier update, and (iii) a novel test to check whether the penalty parameter of the AL function should be updated. Under a basic Slater point condition and some requirements on the dampening factor and under-relaxation parameter, it is shown that DP.ADMM obtains an approximate first-order stationary point of the constrained problem in O(ε-3) iterations for a given numerical tolerance ε > O. One of the main novelties of the paper is that convergence of the method is obtained without requiring any rank assumptions on the constraint matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. A Relaxation Approach to Feature Selection for Linear Mixed Effects Models.
- Author
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Sholokhov, Aleksei, Burke, James V., Santomauro, Damian F., Zheng, Peng, and Aravkin, Aleksandr
- Subjects
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FEATURE selection , *PANEL analysis , *NONCONVEX programming , *PYTHON programming language , *DATA analysis , *DATA modeling , *COHORT analysis - Abstract
Linear Mixed-Effects (LME) models are a fundamental tool for modeling correlated data, including cohort studies, longitudinal data analysis, and meta-analysis. Design and analysis of variable selection methods for LMEs is more difficult than for linear regression because LME models are nonlinear. In this article we propose a novel optimization strategy that enables a wide range of variable selection methods for LMEs using both convex and nonconvex regularizers, including l 1 , Adaptive- l 1 , SCAD, and l 0 . The computational framework only requires the proximal operator for each regularizer to be readily computable, and the implementation is available in an open source python package pysr3, consistent with the sklearn standard. The numerical results on simulated data sets indicate that the proposed strategy improves on the state of the art for both accuracy and compute time. The variable selection techniques are also validated on a real example using a data set on bullying victimization. for this article are available online. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Image Splicing Forgery Detection Using Feature-Based of Sonine Functions andDeep Features.
- Author
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Al-Shamasneh, Ala'a R. and Ibrahim, Rabha W.
- Subjects
PIXELS ,FORGERY ,FEATURE extraction ,SUPPORT vector machines ,DIGITAL images ,NONCONVEX programming ,IMAGE analysis - Abstract
The growing prevalence of fake images on the Internet and social media makes image integrity verification a crucial research topic. One of the most popular methods for manipulating digital images is image splicing, which involves copying a specific area from one image and pasting it into another. Attempts were made to mitigate the effects of image splicing, which continues to be a significant research challenge. This study proposes a new splicing detectionmodel, combining Sonine functions-derived convex-based features and deep features. Two stages make up the proposed method. The first step entails feature extraction, then classification using the "support vector machine" (SVM) to differentiate authentic and spliced images. The proposed Sonine functions-based feature extraction model reveals the spliced texture details by extracting some clues about the probability of image pixels. The proposed model achieved an accuracy of 98.93% when tested with the CASIA V2.0 dataset "Chinese Academy of Sciences, Institute of Automation" which is a publicly available dataset for forgery classification. The experimental results show that, for image splicing forgery detection, the proposed Sonine functions-derived convex-based features and deep features outperform state-of-the-art techniques in terms of accuracy, precision, and recall. Overall, the obtained detection accuracy attests to the benefit of using the Sonine functions alongside deep feature representations. Finding the regions or locations where image tampering has taken place is limited by the study. Future research will need to look into advanced image analysis techniques that can offer a higher degree of accuracy in identifying and localizing tampering regions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. A MODIFICATION PIECEWISE CONVEXIFICATION METHOD WITH A CLASSIFICATION STRATEGY FOR BOX-CONSTRAINED NON-CONVEX OPTIMIZATION PROGRAMS.
- Author
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QIAO ZHU, LIPING TANG, and XINMIN YANG
- Subjects
NONCONVEX programming ,MATHEMATICAL optimization ,MATHEMATICAL formulas ,MATHEMATICAL analysis ,COMPUTER algorithms - Abstract
This paper presents a piecewise convexification method with a box classification strategy to approximate the entire globally optimal solution set of non-convex optimization problems with box constraints. First, the box classification strategy is proposed based on the convexity of the objective function on the sub-boxes, which helps to reduce the number of box divisions and improve the computational efficiency. At the same time, we construct the piecewise convexification problem of the original non-convex optimization problem by applying the α-based Branch-and-Bound (a BB) method, and we define the (approximate) solution set of the piecewise convexification problem based on the result of classifying the sub-boxes. Then, it is deduced that the globally optimal solution set can be approximated by the (approximate) solution set of the piecewise convexification problem. Finally, a piecewise convexification algorithm is proposed that includes a new subset selection technique for division and two new termination tests. The results of our experiments demonstrate the effectiveness and general superiority of our approach over the competition. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. An obstacle-avoidance inverse kinematics method for robotic manipulator in overhead multi-line environment
- Author
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Pengju Yang, Feng Shen, Dingjie Xu, Bingxing Chen, Ronghai Liu, and Hongwu Wang
- Subjects
Inverse kinematics ,Obstacle avoidance ,Robotic manipulator ,Nonconvex programming ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
The inverse kinematics problem plays a crucial role in robotic manipulator planning, autonomous control, and object grasping. This problem can be solved in simple environments based on existing studies. However, it is still challenging to quickly find a feasible inverse kinematic solution when obstacle avoidance is required. In this paper, we present a nonconvex composite programming method to solve the inverse kinematics problem with overhead obstacle-avoidance requirements. Our method enables efficient obstacle avoidance by directly calculating the minimum distance between the manipulator and the overhead environment. We construct end-effector error functions based on the Product of Exponentials model and explicitly provide their gradient formula. We derive the minimum distance based on the geometry parametric equation and directly utilize it to construct the obstacle avoidance function. We propose an enhanced version of adaptive moment estimation based on short-time gradient information to improve optimization performance. Finally, we conduct simulations and experiments in overhead line environments. Comparative results with other optimization methods demonstrate that our proposed method achieves a high success rate with a low solution time.
- Published
- 2024
- Full Text
- View/download PDF
28. Optimality conditions for Tucker low-rank tensor optimization.
- Author
-
Luo, Ziyan and Qi, Liqun
- Subjects
PATTERN recognition systems ,LOW-rank matrices ,NONSMOOTH optimization ,COMPUTER vision ,MATHEMATICAL optimization ,SIGNAL processing ,NONCONVEX programming - Abstract
Optimization problems with tensor variables are widely used in statistics, machine learning, pattern recognition, signal processing, computer vision, etc. Among these applications, the low-rankness of tensors is an intrinsic property that can help unearth potential but important structure or feature in the corresponding high-dimensional multi-way datasets, leading to the study on low-rank tensor optimization (LRTO for short). For the general framework of LRTO, little has been addressed in optimization theory. This motivates us to study the optimality conditions, with special emphasis on the Tucker low-rank constrained problems and the Tucker low-rank decomposition-based reformulations. It is noteworthy that all the involved optimization problems are nonconvex, and even discontinuous, due to the complexity of the tensor Tucker rank function or the multi-linear decomposition with the orthogonality or even group sparsity constraints imposed on factor matrices. By employing the tools in variational analysis, especially the normal cones to low-rank matrices and the properties of matrix manifolds, we propose necessary and/or sufficient optimality conditions for Tucker low-rank tensor optimization problems, which will enrich the context of the nonconvex and nonsmooth optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. UAV Relay Energy Consumption Minimization in an MEC-Assisted Marine Data Collection System.
- Author
-
Xu, Woping and Gu, Li
- Subjects
ENERGY consumption ,TELECOMMUNICATION systems ,ACQUISITION of data ,DRONE aircraft ,BROADBAND communication systems ,MOBILE computing ,NONCONVEX programming - Abstract
Recently, unmanned aerial vehicle (UAV)-assisted maritime communication systems have drawn considerable attention due to their potential for broadband maritime communication applications. However, their limited energy resources remains a critical issue in providing long-term data transmission support for maritime applications. In this study, an integrated sea–air–terrestrial communication system was constructed for marine data collection, where several unmanned surface vessels (USVs) are deployed to collect marine data from underwater sensors (UWSs), and a UAV hovers above these USVs as a relay node, transmitting marine data from USVs to an onshore base station (BS). To prolong the lifetime of the UAV relay, mobile edge computing technology is applied in USVs for partial data computing, which reduces the to-be-relayed data volume from UAVs to USVs to onshore BS as well as the relay energy consumption of UAV. A parallel data computing and transmission scheme was developed for simultaneous local data computing and relaying in the proposed system. Accordingly, a UAV energy consumption minimization problem was formulated with constraints on the USV's computational ability, the USV's transmission power budget, the UAV transmission power budget, and the maximum system latency. To effectively solve this nonconvex optimal problem, an energy optimal partial data computing and relaying strategy was constructed by successively optimizing the data partial computational offloading ratio, USV transmit power allocation, and UAV transmit power. Numerical simulations were used to verify the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. A Customized ADMM Approach for Large-Scale Nonconvex Semidefinite Programming.
- Author
-
Sun, Chuangchuang
- Subjects
- *
NONCONVEX programming , *SEMIDEFINITE programming , *IMAGE segmentation , *MATRIX decomposition , *SYMMETRIC matrices , *SCALABILITY - Abstract
We investigate a class of challenging general semidefinite programming problems with extra nonconvex constraints such as matrix rank constraints. This problem has extensive applications, including combinatorial graph problems, such as MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints. A customized approach based on the alternating direction method of multipliers (ADMM) is proposed to solve the general large-scale nonconvex semidefinite programming efficiently. We propose two reformulations: one using vector variables and constraints, and the other further reformulating the Burer–Monteiro form. Both formulations admit simple subproblems and can lead to significant improvement in scalability. Despite the nonconvex constraint, we prove that the ADMM iterates converge to a stationary point in both formulations, under mild assumptions. Additionally, recent work suggests that in this matrix form, when the matrix factors are wide enough, the local optimum with high probability is also the global optimum. To demonstrate the scalability of our algorithm, we include results for MAX-CUT, community detection, and image segmentation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. 2×2-Convexifications for convex quadratic optimization with indicator variables.
- Author
-
Han, Shaoning, Gómez, Andrés, and Atamtürk, Alper
- Subjects
- *
NONCONVEX programming , *SEMIDEFINITE programming , *INTEGER programming , *QUADRATIC programming , *GLOBAL optimization - Abstract
In this paper, we study the convex quadratic optimization problem with indicator variables. For the 2 × 2 case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the 2 × 2 case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including the optimal perspective relaxation and the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. Robust Adaptive Beamformer Based on Constant Modulus Penalty Criteria.
- Author
-
Hao, Chuanhui, Zhang, Bin, and Sun, Xubao
- Subjects
- *
GLOBAL Positioning System , *ARRAY processing , *NONCONVEX programming , *ANTENNA arrays , *QUADRATIC programming - Abstract
In this study, a robust adaptive beamformer based on constant modulus (CM) criteria is developed to improve the robustness of the array beamforming, which is a reconstructing minimal optimization for solving the mismatch problem of weight vector caused by steering vector mismatch. In the global positioning system (GPS) L1 band, firstly, a GPS array signal is modelled by designing a dual-polarized antenna array. Secondly, the distortion problem of beamforming is formulated in the traditional minimum variance distortionless response (MVDR) beamformer. For repairing the weight vector mismatch problem, a novel beamformer based on the CM envelope response is proposed to reconstruct MVDR beamforming in the array processing. Besides, min-max penalty criteria are used to enable the beamformer to allocate more degrees of freedom (DOFs) when penalizing the MVDR beamformer responses. Finally, an auxiliary two-element real variable is designed to plan the proposed beamformer. But it is still a nonconvex quadratic programming problem, so an alternating direction method of multipliers (ADMM) is employed to transform the objective function into several subproblems. Illustrative numerical simulation results are provided for validating the effectiveness of the proposed beamformer by comparing it with other existing approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. Utopia constrained multi objective optimisation evolutionary algorithm.
- Author
-
Varshini, P. R., Baskar, S., and Tamil Selvi, S.
- Subjects
- *
OPTIMIZATION algorithms , *EVOLUTIONARY algorithms , *NONCONVEX programming , *UTOPIAS - Abstract
A new multiobjective evolutionary optimisation algorithm (MOEA) to solve multimodal, multidimensional, nonconvex, nonlinear, dynamic multiobjective optimisation problems (MOPs) is the need of the hour. The quality of an MOEA lies in a good balance between the exploration and exploitation stages of the MOEA. Utopia constrained MOEA (U-MOEA) is proposed in this paper that improves the exploitation in the replacement step to achieve a perfect balance between exploration and exploitation. The proposed U-MOEA is tested on benchmark MOPs and a multivariable controller design problem. The performance of the proposed algorithm is also compared with other MOEAs such as NSGA-II and ICMDRA concerning hyper volume, nondomination count, combined Pareto set metric, and Cmetric. The performance metrics show better hyper volume and spread metric values for the proposed algorithm, indicating the ability in attaining trade-off region closeness along with diversified Pareto front for U-MOEA when compared to the other two algorithms. Results clearly show that the proposed U-MOEA produces good convergence, diversity characteristics with many numbers of trade-off solutions in a Pareto front. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Effective design and implementation of hybrid renewable system using convex programming.
- Author
-
De Britto C, John, S. Nagarajan, and R. Senthil Kumar
- Subjects
MICROGRIDS ,HYBRID power ,GRIDS (Cartography) ,ELECTRIC power distribution grids ,OPTIMIZATION algorithms ,ENERGY storage ,CONVEX programming ,NONCONVEX programming - Abstract
This manuscript deals with the energy storage technology with renewable energy design can directly reduce the overall constraint of electrical micro grid in upcoming power grids. The original energy monitoring arrangement can lower the typical price of micro grids and increase the utilization of renewable assets by targeting the entire site for essential energy storage systems to predefined functions. The limited progress of solar PV and wind turbines with nickel-cadmium battery storage integrates with the sum of increasing renewable systems, for this concept the hybrid integrated micro grids can be fundamentally modeled and calculated. The proposed hybrid micro grid system gives a photovoltaic output power of 37 kW, the developed output voltage is 80 V and the power of the wind module is 900 watts, the output power of the PV panel is 420 watts. The developed output voltage is 80 V. The convex coding system is used for schema planning and optimization route. The nominal time-optimal controller and receiver locations are simply well known by this planned convex programming method. An optimization algorithm was functional to define the optimal sizing of the PV/wind/battery hybrid system for power continuity in rural areas for continuity of electricity consumption. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. Automated resonance evaluation; Non-convex decomposition method for resonance regression and uncertainty quantification.
- Author
-
Walton, Noah, Armstrong, Jordan, Medal, Hugh, and Sobes, Vladimir
- Subjects
- *
REGRESSION analysis , *MIXED integer linear programming , *RESONANCE , *NONCONVEX programming , *MATHEMATICAL optimization - Abstract
This work serves as a proof of concept for an automated tool to assist in the evaluation of experimental neutron cross section data in the resolved resonance range. The resonance characterization problem is posed as a mixed integer nonlinear program (MINLP). Since the number of resonances present is unknown, the model must be able to be determine the number of parameters to properly characterize the cross section curve as well as calculate the appropriate values for those parameters. Due to the size of the problem and the nonconvex nature of the parameterization, the optimization formulation is too difficult to solve as whole. A novel method is developed to decompose the problem into smaller, solvable windows and then stitch them back together via parameter-cardinality and parameter-value agreement routines in order to achieve a global solution. A version of quantile regression is used to provide an uncertainty estimate on the suggested cross section that is appropriate with respect to the experimental data. The results demonstrate the model's ability to find the proper number of resonances, appropriate average values for the parameters, and an uncertainty estimation that is directly reflective of the experimental conditions. The use of synthetic data allows access to the solution, this is leveraged to build-up performance statistics and map the uncertainty driven by the experimental data to an uncertainty on the true cross section. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Acceleration in first-order optimization methods : promenading beyond convexity or smoothness, and applications
- Author
-
Martinez Rubio, David, Kanade, Varun, and Rebeschini, Patrick
- Subjects
Nonsmooth optimization ,Structural optimization ,Nonconvex programming - Abstract
Acceleration in optimization is a term that is generally applied to optimization algorithms presenting some common methodology that enjoy convergence rates that improve over other more simple algorithms for the same problem. For example, Nesterov's Accelerated Gradient Descent improves over the gradient descent method for the optimization of smooth and convex functions. In this thesis, we investigate the acceleration phenomenon and its applications for three previously studied research questions in optimization and online learning: geodesically convex accelerated optimization in Riemannian manifolds, approximation of a proportional fair solution under positive linear constraints, also known as the 1-fair packing problem, and regret minimization in a decentralized cooperative stochastic multi-armed bandit problem with no reward collisions. We improve over previously studied approaches by using acceleration as a key element in all of our algorithms: we obtain an accelerated method for some non-convex problems in the first case, we exploit a local decrease condition of our problem in the second case, avoiding the use of poor and non-global smoothness, and in the third problem, we design a solution for which we can effectively apply an accelerated gossip protocol to spread and use information. In particular, we provide an extensive overview of acceleration techniques that provide context for ours proofs. In Riemannian optimization, we design the first global accelerated algorithm for the optimization of smooth functions that are geodesically convex or geodesically strongly convex and that are defined in manifolds of constant sectional curvature. We reduce these problems to a Euclidean non-convex problem and design a global accelerated method, obtaining a solution with the same rates of Accelerated Gradient Descent in the Euclidean space, up to logarithmic factors and constants depending on the initial distance to an optimum and on the curvature. We also provide some reductions. Regarding our fairness problem, we present a deterministic, accelerated, distributed and width-independent algorithm for the 1-fair packing problem. We obtain a quadratic improvement in the number of iterations and remove polylog(width) factors with respect to the previous best solution. In our bandit problem, we design a decentralized upper confidence bound algorithm to minimize the expected regret. It allows for the use of delayed and approximate estimations of the arms' means which we can obtain fast with an accelerated gossip communication protocol. We provide theoretical and empirical comparisons showing we obtain lower regret than previous state of the art.
- Published
- 2021
37. Computing multiple solutions of topology optimization problems
- Author
-
Papadopoulos, Ioannis, Farrell, Patrick, and Süli, Endre
- Subjects
Mathematics ,Finite element method ,Constrained optimization ,Differential equations, Partial ,Nonconvex programming ,Multigrid methods (Numerical analysis) ,Numerical analysis - Abstract
Topology optimization finds the optimal material distribution of a continuum in a domain, subject to PDE and volume constraints. Density-based models often result in a PDE, volume and inequality constrained, nonconvex, infinite-dimensional optimization problem. These problems can exhibit many local minima. In practice, heuristics are used to aid the search for better minima, but these can fail even in the simplest of cases. In this thesis we address two core issues related to the nonconvexity of topology optimization problems: the convergence of the discretization and the computation of the solutions. First, we consider the convergence of a finite element discretization of a fluid topology optimization problem. Results available in literature show that there exists a sequence of finite element solutions that weakly(-*) converges to a solution of the infinite-dimensional problem. We improve on these classical results. In particular, by fixing any isolated minimizer, we show that there exists a sequence of finite element solutions that \emph{strongly} converges to that minimizer. Moreover, these results hold for both traditional conforming finite element methods and more sophisticated divergence-free discontinuous Galerkin finite element methods. We then focus on developing a solver that can systematically compute multiple minimizers of a general density-based topology optimization problem. This leads to the successful computation of 42 distinct solutions of a two-dimensional fluid topology optimization problem. Finally, by developing preconditioners for the linear systems that arise during the optimization process, we are able to apply the solver to three-dimensional fluid topology optimization problems. This culminates in an example where we compute 11 distinct three-dimensional solutions.
- Published
- 2021
38. An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization.
- Author
-
Yang, Heng, Liang, Ling, Carlone, Luca, and Toh, Kim-Chuan
- Subjects
- *
NONLINEAR programming , *NONCONVEX programming , *SEMIDEFINITE programming , *POLYNOMIALS - Abstract
We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new algorithmic framework that blends local search using the nonconvex POP into global descent using the convex SDP. In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework. We then accelerate iPGM by taking long, but safeguarded, rank-one steps generated by fast nonlinear programming algorithms. We prove that the new framework is still globally convergent for solving the SDP. To solve the iPGM subproblem of projecting a given point onto the feasible set of the SDP, we design a two-phase algorithm with phase one using a symmetric Gauss–Seidel based accelerated proximal gradient method (sGS-APG) to generate a good initial point, and phase two using a modified limited-memory BFGS (L-BFGS) method to obtain an accurate solution. We analyze the convergence for both phases and establish a novel global convergence result for the modified L-BFGS that does not require the objective function to be twice continuously differentiable. We conduct numerical experiments for solving second-order SDP relaxations arising from a diverse set of POPs. Our framework demonstrates state-of-the-art efficiency, scalability, and robustness in solving degenerate SDPs to high accuracy, even in the presence of millions of equality constraints. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
39. Supermodularity and valid inequalities for quadratic optimization with indicators.
- Author
-
Atamtürk, Alper and Gómez, Andrés
- Subjects
- *
SET functions , *QUADRATIC forms , *NONCONVEX programming , *NONLINEAR functions , *QUADRATIC programming , *MODULAR forms , *QUADRATIC differentials - Abstract
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult, the specific set function for the rank-one quadratic can be minimized in linear time. We show that the convex hull of the epigraph of the quadratic can be obtained from inequalities for the underlying supermodular set function by lifting them into nonlinear inequalities in the original space of variables. Explicit forms of the convex-hull description are given, both in the original space of variables and in an extended formulation via conic quadratic-representable inequalities, along with a polynomial separation algorithm. Computational experiments indicate that the lifted supermodular inequalities in conic quadratic form are quite effective in reducing the integrality gap for quadratic optimization with indicators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
40. Inference for low‐ and high‐dimensional inhomogeneous Gibbs point processes.
- Author
-
Ba, Ismaïla and Coeurjolly, Jean‐François
- Subjects
- *
POINT processes , *ASYMPTOTIC normality , *FEATURE selection , *NONCONVEX programming , *INFERENTIAL statistics , *STATISTICAL models - Abstract
Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high‐dimensional statistical modeling. In this paper, a composite likelihood (in particular pseudo‐likelihood) approach regularized with convex and nonconvex penalty functions is proposed to handle statistical inference for possibly high‐dimensional inhomogeneous GPPs. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on penalty functions, we show that the oracle property, consistency and asymptotic normality hold. Our results also cover the low‐dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. On solving difference of convex functions programs with linear complementarity constraints.
- Author
-
Le Thi, Hoai An, Nguyen, Thi Minh Tam, and Dinh, Tao Pham
- Subjects
COMPLEMENTARITY constraints (Mathematics) ,LINEAR complementarity problem ,CONVEX functions ,NONCONVEX programming ,DIFFERENTIABLE functions - Abstract
We address a large class of Mathematical Programs with Linear Complementarity Constraints which minimizes a continuously differentiable DC function (Difference of Convex functions) on a set defined by linear constraints and linear complementarity constraints, named Difference of Convex functions programs with Linear Complementarity Constraints. Using exact penalty techniques, we reformulate it, via four penalty functions, as standard Difference of Convex functions programs. The difference of convex functions algorithm (DCA), an efficient approach in nonconvex programming framework, is then developed to solve the resulting problems. Two particular cases are considered: quadratic problems with linear complementarity constraints and asymmetric eigenvalue complementarity problems. Numerical experiments are performed on several benchmark data, and the results show the effectiveness and the superiority of the proposed approaches comparing with some standard methods. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints.
- Author
-
Luo, Hezhi, Zhang, Xianye, Wu, Huixian, and Xu, Weiqiang
- Subjects
NONCONVEX programming ,QUADRATIC programming ,ALGORITHMS ,TABU search algorithm ,SEARCH algorithms - Abstract
We consider in this paper a separable and nonconvex quadratic program (QP) with a quadratic constraint and a box constraint that arises from application in optimal portfolio deleveraging (OPD) in finance and is known to be NP-hard. We first propose an improved Lagrangian breakpoint search algorithm based on the secant approach (called ILBSSA) for this nonconvex QP, and show that it converges to either a suboptimal solution or a global solution of the problem. We then develop a successive convex optimization (SCO) algorithm to improve the quality of suboptimal solutions derived from ILBSSA, and show that it converges to a KKT point of the problem. Second, we develop a new global algorithm (called ILBSSA-SCO-BB), which integrates the ILBSSA and SCO methods, convex relaxation and branch-and-bound framework, to find a globally optimal solution to the underlying QP within a pre-specified ϵ -tolerance. We establish the convergence of the ILBSSA-SCO-BB algorithm and its complexity. Preliminary numerical results are reported to demonstrate the effectiveness of the ILBSSA-SCO-BB algorithm in finding a globally optimal solution to large-scale OPD instances. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Dislocation hyperbolic augmented Lagrangian algorithm for nonconvex optimization.
- Author
-
Ramirez, Lennin Mallma, Maculan, Nelson, Xavier, Adilson Elias, and Xavier, Vinicius Layter
- Subjects
NONCONVEX programming ,NONLINEAR programming ,ALGORITHMS - Abstract
The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity condition. in this work, we ensure that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point, and we present computational experiments to demonstrate the performance of our proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. New semidefinite relaxations for a class of complex quadratic programming problems.
- Author
-
Xu, Yingzhe, Lu, Cheng, Deng, Zhibin, and Liu, Ya-Feng
- Subjects
QUADRATIC programming ,SEMIDEFINITE programming ,NONCONVEX programming ,APPROXIMATION algorithms ,COMPUTER performance ,SIGNAL processing - Abstract
In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the matrix variables in the lifted space, we derive some enhanced semidefinite relaxations of the complex quadratic programming problems. Then, we compare the proposed semidefinite relaxations with existing ones, and show that the newly proposed semidefinite relaxations could be strictly tighter than the previous ones. Moreover, the proposed semidefinite relaxations can be applied to more general cases of complex quadratic programming problems, whereas the previous ones are only designed for special cases. Numerical results indicate that the proposed semidefinite relaxations not only provide tighter relaxation bounds, but also improve some existing approximation algorithms by finding better sub-optimal solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Hydropower Unit Commitment Using a Genetic Algorithm with Dynamic Programming.
- Author
-
Liu, Shuangquan, Wang, Pengcheng, Xu, Zifan, Feng, Zhipeng, Zhang, Congtong, Wang, Jinwen, and Chen, Cheng
- Subjects
- *
DYNAMIC programming , *GENETIC algorithms , *WATER power , *NONCONVEX programming , *GENETIC programming , *UNITS of time - Abstract
This study presents a genetic algorithm integrated with dynamic programming to address the challenges of the hydropower unit commitment problem, which is a nonlinear, nonconvex, and discrete optimization, involving the hourly scheduling of generators in a hydropower system to maximize benefits and meet various constraints. The introduction of a progressive generating discharge allocation enhances the performance of dynamic programming in fitness evaluations, allowing for the fulfillment of various constraints, such as unit start-up times, shutdown/operating durations, and output ranges, thereby reducing complexity and improving the efficiency of the genetic algorithm. The application of the genetic algorithm with dynamic programming and progressive generating discharge allocation at the Manwan Hydropower Plant in Yunnan Province, China, showcases increased flexibility in outflow allocation, reducing spillages by 79%, and expanding high-efficiency zones by 43%. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Clustering Methods over the Tropical Projective Torus.
- Author
-
Barnhill, David and Yoshida, Ruriko
- Subjects
- *
TORUS , *HIERARCHICAL clustering (Cluster analysis) , *K-means clustering , *PHYLOGENY , *NONCONVEX programming - Abstract
In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means and hierarchical clustering in the Euclidean space. We provide results from computational experiments on generic simulated data as well as an application to phylogeny using ultrametrics, demonstrating the efficacy of these methods. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Combined heat and power economic dispatch problem with binary method using flower pollination algorithm and differential evolution.
- Author
-
Mellal, Mohamed Arezki, Khitous, Marwa, and Zemmouri, Meriem
- Subjects
- *
DIFFERENTIAL evolution , *PARTICLE swarm optimization , *ALGORITHMS , *FLOWERS , *ELECTRICAL energy , *NONCONVEX programming - Abstract
Nowadays, the need for electrical energy became crucial in the world. The co-generation plants, which simultaneously produce electrical and heat energies, are one of the alternative solutions to supply people and industry with both energies. The present work addresses the cost minimization of the nonconvex combined heat and power dispatch problem (CHPED). The nonconvex operating region is handled using the binary method, and the optimization problem is solved using two nature-inspired algorithms, namely the flower pollination algorithm (FPA) and the differential evolution (DE). Penalty functions are adopted to handle all the operating constraints, units' limits, and demands. The results obtained compare the algorithms and those of the literature. It is observed that the fuel cost obtained by the flower pollination algorithm (FPA) is less than the one obtained by the differential evolution (DE) and the particle swarm optimization (PSO). [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. An optimized nonlinear generalized predictive control for steam temperature in an ultra supercritical unit.
- Author
-
Cheng, Chuanliang, Peng, Chen, Zhang, Tengfei, and Zeng, Deliang
- Subjects
TEMPERATURE control ,OPTIMIZATION algorithms ,MACHINE learning ,NONCONVEX programming ,LEARNING ,ITERATIVE learning control ,LINEAR network coding ,QUADRATIC programming - Abstract
The optimize control of the ultra supercritical (USC) unit has been a major concern in power industry. The intermediate point temperature process is a multi-variable system with strong nonlinearity, large scale and great delay, which greatly affects the safety and economy of the USC unit. Generally, it is difficult to realize effective control by using conventional methods. This paper presents a nonlinear generalized predictive control based on a composite weighted human learning optimization network (CWHLO-GPC) to improve the control performance of intermediate point temperature. Based on the characteristics of the onsite measurement data, the heuristic information is incorporated into the CWHLO network, and expressed by different local linear models. Then, global controller is elaborately constituted based on a scheduling program inferred from the network. Compared with classical generalized predictive control (GPC), the non-convex problem is effectively solved by introducing CWHLO models into the convex quadratic program (QP) routine of local linear GPC. Finally, detailed analysis on set point tracking and interference resisting via simulation is addressed to illustrate the efficiency of the proposed strategy. • A network with self-learning and self-organizing abilities is delicately constructed. Through reasonable partition, the nonlinearity of the object system is diluted to an acceptable range. • Real-coded human learning optimization algorithm is first proposed and applied to local linear modeling, by which more accurate models are obtained. • An improved generalized predictive control algorithm is proposed based on local models. And by the mutual cooperation of local controllers, the problem of non-convex in quadratic programming is effectively solved. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints.
- Author
-
Xu, Zhuoyi, Li, Linbin, and Xia, Yong
- Subjects
NONCONVEX programming ,APPROXIMATION algorithms ,QUADRATIC forms ,INTEGERS ,ELLIPSOIDS - Abstract
An efficient partial ellipsoid approximation scheme is presented to find a 1 ⌈ m 2 ⌉ -approximation solution to the nonconvex homogeneous quadratic optimization with m convex quadratic constraints, where ⌈ x ⌉ is the smallest integer larger than or equal to x. If there is an additional nonconvex quadratic constraint beyond the m convex constraints, we can use the new scheme to find a 1 m -approximation solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. IRS 辅助 WPCN 用户公平性与系统吞吐量优化方案.
- Author
-
丰敏 and 朱江
- Subjects
REFLECTANCE ,MATHEMATICAL optimization ,PROBLEM solving ,FAIRNESS ,WIRELESS communications ,NONCONVEX programming - Abstract
Copyright of Journal of Chongqing University of Posts & Telecommunications (Natural Science Edition) is the property of Chongqing University of Posts & Telecommunications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2023
- Full Text
- View/download PDF
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