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We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility. [ABSTRACT FROM AUTHOR]

We study the image of SU (n) under the diagonal product map. Using only elementary tools of linear algebra, analysis and general topology, we find the analytical formula for the boundary of this image and find all special unitary matrices whose diagonal product lies on that boundary. [ABSTRACT FROM AUTHOR]

Human beings always engage in a vast range of activities and tasks that demonstrate their ability to adapt to different scenarios. These activities can range from the simplest daily routines, like walking and sitting, to multi-level complex endeavors such as cooking a four-course meal. Any human activity can be represented as a temporal sequence of actions performed to achieve a certain goal. Unlike the time series datasets extracted from electronics or machines, these action sequences are highly disparate in their nature—the time to finish a sequence of actions can vary between different persons. Therefore, understanding the dynamics of these sequences is essential for many downstream tasks such as activity length prediction, goal prediction, and next action recommendation. Existing neural network based approaches that learn a continuous-time activity sequence are limited to the presence of only visual data or are designed specifically for a particular task (i.e., limited to next action or goal prediction). In this article, we present ProActive, a neural marked temporal point process framework for modeling the continuous-time distribution of actions in an activity sequence while simultaneously addressing three high-impact problems: next action prediction, sequence goal prediction, and end-to-end sequence generation. Specifically, we utilize a self-attention module with temporal normalizing flows to model the influence and the inter-arrival times between actions in a sequence. Moreover, for time-sensitive prediction, we perform an early detection of sequence goal via a constrained margin-based optimization procedure. This in turn allows ProActive to predict the sequence goal using a limited number of actions. In addition, we propose a novel addition over the ProActive model, called ProActive++, that can handle variations in the order of actions (i.e., different methods of achieving a given goal). We demonstrate that this variant can learn the order in which the person or actor prefers to do their actions. Extensive experiments on sequences derived from three activity recognition datasets show the significant accuracy boost of our ProActive and ProActive++ over the state of the art in terms of action and goal prediction, and the first-ever application of end-to-end action sequence generation. [ABSTRACT FROM AUTHOR]

Image enhancement is a vital process that serves as a tool for improving the quality of a lot of real-life applications. Fractional calculus can be utilized in enhancing images using fractional order kernels, adding more controllability to the system, due to the flexible choice of the fractional order parameter, which adds extra degrees of freedom. The proposed system merges two fractional order kernels which helps in image enhancement techniques, and the contribution of this work is based on the study of how to optimize this process. The optimization of the two fractional kernels was done using the neural network optimization algorithm (NNA) to utilize the best order for the two kernels. In this paper, three fractional kernels are studied to highlight the performance of image enhancement using fractional kernels against different metrics. Furthermore, three different combinations of two kernels are combined and studied to enhance the metrics score by utilizing two different fractional orders for each kernel. Various optimization algorithms are used to obtain the optimum fractional order for both single and combined kernels. Using the constrained NNA, the evaluation metrics of the image enhancement show a 33% increase in measure of enhancement metric (EME), 21% increase in contrast, and 4% increase in average gradient compared to the best-achieved metrics by the literature while keeping the similarity metric above 0.75. [ABSTRACT FROM AUTHOR]

This paper presents improved single- and multi-objective algorithms based on the original moth flame optimizer (MFO) to tackle the dynamic economic emission dispatch (DEED) problem that affects power systems operations. The DEED problem is a multi-objective optimization problem that is strongly constrained, multi-dimensional, nonlinear, and non-convex. It comprises several optimization criteria, many of which are in direct opposition to one another; therefore, no one solution is optimal with regard to all of those criteria. Firstly, an enhanced flame generation strategy is incorporated into the MFO algorithm to improve performance. Then, the improved MFO is combined with the crowding distance mechanism and non-dominated sorting framework to enhance the convergence rate and the quality of the results. This helps improve the convergence pace. Firstly, the proposed multi-objective moth flame optimizer (MOMFO) algorithm is validated using 15 ZDT and UF benchmark multi-objective test functions. Then, the nonlinear DEED problem is also solved by determining the feasible optimal solution using the MOMFO algorithm. The implementation of the MOMFO on 10-unit systems and the IEEE 30-bus test system is being done to display the ability to solve a nonlinear, non-convex, and constrained DEED optimization problem. The DEED problem is solved using the MOMFO algorithm and other state-of-the-art algorithms, such as the non-dominated sorting genetic algorithm-II (NSGA-II), the multi-objective teaching–learning-based optimization (MOTLBO) algorithm, and multi-objective reptile search algorithm (MORSA). The selection of the control parameters of the MOMFO can be decided from the algorithm's findings on different IEEE bus systems. This study also introduces a new technique for incorporating loss predictions using artificial neural networks into the DEED model. During each phase of the dispatch time, the trained neural network can make only a single forecast of the transmission loss. The performance of MOMFO is compared with NSGA-II, MOTLBO, and MORSA, and the results obtained for both benchmarks and DEED proved the superiority of the proposed algorithm in solving the DEED of the power systems. [ABSTRACT FROM AUTHOR]

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization. [ABSTRACT FROM AUTHOR]

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition. [ABSTRACT FROM AUTHOR]

BACKGROUND: The scientific revolution in the treatment of many illnesses has been significantly aided by stem cells. This paper presents an optimal control on a mathematical model of chemotherapy and stem cell therapy for cancer treatment. OBJECTIVE: To develop effective hybrid techniques that combine the optimal control theory (OCT) with the evolutionary algorithm and multi-objective swarm algorithm. The developed technique is aimed to reduce the number of cancerous cells while utilizing the minimum necessary chemotherapy medications and minimizing toxicity to protect patients' health. METHODS: Two hybrid techniques are proposed in this paper. Both techniques combined OCT with the evolutionary algorithm and multi-objective swarm algorithm which included MOEA/D, MOPSO, SPEA II and PESA II. This study evaluates the performance of two hybrid techniques in terms of reducing cancer cells and drug concentrations, as well as computational time consumption. RESULTS: In both techniques, MOEA/D emerges as the most effective algorithm due to its superior capability in minimizing tumour size and cancer drug concentration. CONCLUSION: This study highlights the importance of integrating OCT and evolutionary algorithms as a robust approach for optimizing cancer chemotherapy treatment. [ABSTRACT FROM AUTHOR]

In the smooth constrained optimization setting, this work introduces the Domain Complementary Approximate Karush–Kuhn–Tucker (DCAKKT) condition, inspired by a sequential optimality condition recently devised for non-smooth constrained optimization problems. It is shown that the augmented Lagrangian method can generate limit points satisfying DCAKKT, and it is proved that such a condition is not related to previously established sequential optimality conditions. An essential characteristic of the DCAKKT is to capture the asymptotic potential increasing of the Lagrange multipliers using a single parameter. Besides that, DCAKKT points satisfy the Strong Approximate Gradient Projection (SAGP) condition. Due to the intrinsic features of DCAKKT, which combine strength and generality, this novel and genuine sequential optimality condition may shed some light upon the practical performance of algorithms that are yet to be devised. [ABSTRACT FROM AUTHOR]

In this two-part study, we develop a general theory of the so-called exact augmented Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to traditional nonsmooth exact penalty functions, these augmented Lagrangians are continuously differentiable for smooth problems and do not suffer from the Maratos effect, which makes them especially appealing for applications in numerical optimization. Our aim is to present a detailed study of various theoretical properties of exact augmented Lagrangians and discuss several applications of these functions to constrained variational problems, problems with PDE constraints, and optimal control problems. The first paper is devoted to a theoretical analysis of an exact augmented Lagrangian for optimization problems in Hilbert spaces. We obtain several useful estimates of this augmented Lagrangian and its gradient, and present several types of sufficient conditions for KKT-points of a constrained problem corresponding to locally/globally optimal solutions to be local/global minimizers of the exact augmented Lagrangian. [ABSTRACT FROM AUTHOR]

This paper proposes a novel Difference-of-Convex (DC) decomposition for polynomials using a power-sum representation, achieved by solving a sparse linear system. We introduce the Boosted DCA with Exact Line Search ( BDCA e ) for addressing linearly constrained polynomial programs within the DC framework. Notably, we demonstrate that the exact line search equates to determining the roots of a univariate polynomial in an interval, with coefficients being computed explicitly based on the power-sum DC decompositions. The subsequential convergence of BDCA e to critical points is proven, and its convergence rate under the Kurdyka–Łojasiewicz property is established. To efficiently tackle the convex subproblems, we integrate the Fast Dual Proximal Gradient method by exploiting the separable block structure of the power-sum DC decompositions. We validate our approach through numerical experiments on the Mean–Variance–Skewness–Kurtosis portfolio optimization model and box-constrained polynomial optimization problems. Comparative analysis of BDCA e against DCA, BDCA with Armijo line search, UDCA, and UBDCA with projective DC decomposition, alongside standard nonlinear optimization solvers FMINCON and FILTERSD, substantiates the efficiency of our proposed approach. [ABSTRACT FROM AUTHOR]

In the context of the rapid development of the Internet of Vehicles, virtual reality, automatic driving and the industrial Internet, the terminal devices in the network show explosive growth. As a result, more and more information is generated from the edge of the network, which makes the data throughput increase dramatically in the mobile communication network. As the key technology of the fifth-generation mobile communication network, mobile edge caching technology which caches popular data to the edge server deployed at the edge of the network avoids the data transmission delay of the backhaul link and the occurrence of network congestion. With the growing scale of the network, distributing hot data from cloud servers to edge servers will generate huge energy consumption. To realize the green and sustainable development of the communication industry and reduce the energy consumption of distribution of data that needs to be cached in edge servers, we make the first attempt to propose and solve the problem of edge caching data distribution with minimum energy consumption (ECDDMEC) in this paper. First, we model and formulate the problem as a constrained optimization problem and then prove its NP-hardness. Subsequently, we design a greedy algorithm with computational complexity of O (n 2) to solve the problem approximately. Experimental results show that compared with the distribution strategy of each edge server directly requesting data from the cloud server, the strategy obtained by the algorithm can significantly reduce the energy consumption of data distribution. [ABSTRACT FROM AUTHOR]

Background: CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose: This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods: We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results: Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions: PROSPECT algorithm achieved a high degree of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder, and structural magnetic resonance imaging (sMRI) and functional magnetic resonance imaging (fMRI) provide information about brain structure and function, aiding in objective ASD diagnosis. However, existing ASD classification methods face challenges such as sample scarcity, inter‐imaging center variations, insufficient single‐modality information, and inconsistent feature dimensions. This study introduced a method based on the Local Global Multimodal Domain Adaptation (LGMDA)‐Sparse Adaptive Prior Coupled Dictionary Learning (SACDL) framework. Initially, the LGMDA method was introduced to achieve multi‐source DA. By minimizing differences between different data domains while maximizing inter‐class differences within the same domain, it expands the sample size of multi‐modal data, addressing the issues of sample scarcity and heterogeneity in ASD data. Subsequently, the SACDL method was employed for multimodal fusion. It initialized dictionaries using the ATGP algorithm, combined sMRI and fMRI data for dictionary learning, adaptively adjusted sparsity parameters, and integrated ASD phenotype data for constrained optimization. It enables joint learning of shared and modality‐specific features, balancing differences in feature dimensions. Experimental results show that this model effectively utilizes multi‐center, multi‐modal information to achieve better auxiliary diagnosis than single‐modal small samples. This method has the potential to provide effective solutions for ASD multi‐source and multi‐modal classification problems, which are significant for ASD research and clinical diagnosis. [ABSTRACT FROM AUTHOR]

An optimization-based tool for flow predictions in natural rivers is introduced assuming that some physical characteristics of a river within a spatial-time domain [ x min , x max ] × [ t min , t today ] are known. In particular, it is assumed that the bed elevation and width of the river are known at a finite number of stations in [ x min , x max ] and that the flow-rate at x = x min is known for a finite number of time instants in [ t min , t today ] . Using these data, given t future > t today and a forecast of the flow-rate at x = x min and t = t future , a regression-based algorithm informed by partial differential equations produces predictions for all state variables (water elevation, depth, transversal wetted area, and flow-rate) for all x ∈ [ x min , x max ] and t = t future . The algorithm proceeds by solving a constrained optimization problem that takes into account the available data and the fulfillment of Saint-Venant equations for one-dimensional channels. The effectiveness of this approach is corroborated with flow predictions of a natural river. [ABSTRACT FROM AUTHOR]

Adaptive cruise control (ACC) enables efficient, safe, and intelligent vehicle control by autonomously adjusting speed and ensuring a safe following distance from the vehicle in front. This paper proposes a novel adaptive cruise system, namely the Safety-First Reinforcement Learning Adaptive Cruise Control (SFRL-ACC). This system aims to leverage the model-free nature and high real-time inference efficiency of Deep Reinforcement Learning (DRL) to overcome the challenges of modeling difficulties and lower computational efficiency faced by current optimization control-based ACC methods while simultaneously maintaining safety advantages and optimizing ride comfort. Firstly, we transform the ACC problem into a safe DRL formulation Constrained Markov Decision Process (CMDP) by carefully designing state, action, reward, and cost functions. Subsequently, we propose the Projected Constrained Policy Optimization (PCPO)-based ACC Algorithm SFRL-ACC, which is specifically tailored to solve the CMDP problem. PCPO incorporates safety constraints that further restrict the trust region formed by the Kullback–Leibler (KL) divergence, facilitating DRL policy updates that maximize performance while keeping safety costs within their limit bounds. Finally, we train an SFRL-ACC policy and compare its computation time, traffic efficiency, ride comfort, and safety with state-of-the-art MPC-based ACC control methods. The experimental results prove the superiority of the proposed method in the aforementioned performance aspects. [ABSTRACT FROM AUTHOR]

Railway alignment development in a study area with densely-distributed obstacles, in which regions favorable for alignments are isolated (termed an isolated island effect, i.e., IIE), is a computation-intensive and time-consuming task. To enhance search efficiency and solution quality, an environmental suitability analysis is conducted to identify alignment-favorable regions (AFRs), focusing the subsequent alignment search on these areas. Firstly, a density-based clustering algorithm (DBSCAN) and a specific criterion are customized to distinguish AFR distribution patterns: continuously-distributed AFRs, obstructed effects, and IIEs. Secondly, a study area characterized by IIEs is represented with a semantic topological map (STM), integrating between-island and within-island paths. Specifically, between-island paths are derived through a multi-directional scanning strategy, while within-island paths are optimized using a Floyd-Warshall algorithm. To this end, the intricate alignment optimization problem is simplified into a shortest path problem, tackled with conventional shortest path algorithms (of which Dijkstra’s algorithm is adopted in this work). Lastly, the proposed method is applied to a real case in a mountainous region with karst landforms. Numerical results indicate its superior performance in both construction costs and environmental suitability compared to human designers and a prior alignment optimization method. [ABSTRACT FROM AUTHOR]

In this study, we introduce a distributed algorithm that is specifically designed to address optimization problems featuring a decomposable objective function and equality constraints. To minimize the amount of communication required, we incorporate an event-triggered mechanism that enables information exchange only when variable values exceed predefined thresholds. Importantly, our proposed algorithm possesses a distinctive characteristic where the determination of step size is solely based on the properties of the objective function, regardless of the structure of the communication network. Even in situations where changes occur in the network structure, our algorithm remains valid without necessitating any updates to its step size. Assuming strong convexity and smoothness in local objective functions, along with appropriate event-triggered thresholds, our algorithm achieves a convergence rate that is linear. Several numerical experiments provide evidence supporting the effectiveness and superiority of our proposed approach. [ABSTRACT FROM AUTHOR]

Mixture Markov Model (MMM) is a widely used tool to cluster sequences of events coming from a finite state-space. However, the MMM likelihood being multi-modal, the challenge remains in its maximization. Although Expectation-Maximization (EM) algorithm remains one of the most popular ways to estimate the MMM parameters, however, convergence of EM algorithm is not always guaranteed. Given the computational challenges in maximizing the mixture likelihood on the constrained parameter space, we develop a pattern search-based global optimization technique which can optimize any objective function on a collection of simplexes, which is eventually used to maximize MMM likelihood. This is shown to outperform other related global optimization techniques. In simulation experiments, the proposed method is shown to outperform the expectation-maximization (EM) algorithm in the context of MMM estimation performance. The proposed method is applied to cluster Multiple sclerosis (MS) patients based on their treatment sequences of disease-modifying therapies (DMTs). We also propose a novel method to cluster people with MS based on DMT prescriptions and associated clinical features (covariates) using MMM with covariates. Based on the analysis, we divided MS patients into three clusters. Further cluster-specific summaries of relevant covariates indicate patient differences among the clusters. for this article are available online. [ABSTRACT FROM AUTHOR]

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field. [ABSTRACT FROM AUTHOR]

Supply Chain (SC) Optimization is a key activity in today's industry with the goal of increasing operational efficiency, reducing costs, and improving customer satisfaction. Traditional optimization methods often struggle to effectively use resources while handling complex and dynamic Supply chain networks. This paper introduces a novel biomimetic metaheuristic algorithm called the Wombat Optimization Algorithm (WOA) for supply chain optimization. This algorithm replicates the natural behaviors observed in wombats living in the wild, particularly focusing on their foraging tactics and evasive maneuvers towards predators. The theory of WOA is described and then mathematically modeled in two phases: (i) exploration based on the simulation of wombat movements during foraging and trying to find food and (ii) exploitation based on simulating wombat movements when diving towards nearby tunnels to defend against its predators. The effectiveness of WOA in addressing optimization challenges is assessed by handling the CEC 2017 test suite across various problem dimensions, including 10, 30, 50, and 100. The findings of the optimization indicate that WOA demonstrates a strong ability to effectively manage exploration and exploitation, and maintains a balance between them throughout the search phase to deliver optimal solutions for optimization problems. A total of twelve well-known metaheuristic algorithms are called upon to test their performance against WOA in the optimization process. The outcomes of the simulations reveal that WOA outperforms the other algorithms, achieving superior results across most benchmark functions and securing the top ranking as the most efficient optimizer. Using a Wilcoxon rank sum test statistical analysis, it has been proven that WOA outperforms other algorithms significantly. WOA is put to the test with twenty-two constrained optimization problems from the CEC 2011 test suite and four engineering design problems to showcase its ability to solve real-world optimization problems. The results of the simulations demonstrate that WOA excels in real-world applications by delivering superior solutions and outperforming its competitors. [ABSTRACT FROM AUTHOR]

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) is a new approach to the hyperbolic augmented Lagrangian algorithm (HALA). DHALA is designed to solve convex nonlinear programming problems. We guarantee that the sequence generated by DHALA converges towards a Karush-Kuhn-Tucker point. We are going to observe that DHALA has a slight computational advantage in solving the problems over HALA. Finally, we will computationally illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

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]

Orthogonally decomposable (odeco) tensors is a special class of symmetric tensors. Previous works have focused on investigating its E-eigenpairs problem, and made some theoretical achievements concerning the number and the local optimality of E-eigenpairs. However, concerning local optimality of each eigenpair, the existing work only analyzed the third-order tensor case. In this paper, we further exploit this issue for any higher-order tensors by checking second-order necessary condition of the related constrained optimization model and deducing an equivalent matrix formula criterion for local optimality identification. Finally, a generalized conclusion for local optimality of eigenpairs for odeco tensors is provided, and some simulated experiments are conducted for validation. [ABSTRACT FROM AUTHOR]

AbstractPV (photovoltaic) systems, also known as solar panel systems, play an essential role in the mitigation of greenhouse gas emissions and the promotion of renewable energy. Through the conversion of sunlight into usable energy, electricity is generated without emitting greenhouse gases and producing pollutants. Notwithstanding the evolutionary significance of PV systems, the occurrence of defects and anomalies in PV systems may result in diminished power output, consequently impeding the efficiency of the systems and potentially resulting in hazards in certain circumstances. Therefore, early detection of faults and anomalies in PV systems is imperative to guarantee the reliability, efficiency, and safety of the systems. In this paper, we develop a signal decomposition for the purpose of anomaly detection in PV systems. The proposed methodology is grounded on the concept of low-rank and sparse decomposition, with consideration given to the signs of the decomposed low-rank and sparse components, as well as the smooth variations within and between periods in the mean signals. Through the implementation of Monte Carlo simulations, we showcase the efficacy of our proposed methodology in identifying anomalies of varying durations and magnitudes in PV systems. A case study is employed to validate the proposed methodology in detecting anomalies in real PV systems. [ABSTRACT FROM AUTHOR]

In this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any decoupling. Self-collisions are modeled in a natural way that allows considering the thickness of cloth without introducing unwanted oscillations. The discretization of the equations of motion leads naturally to a sequence of quadratic problems with inequality and equality constraints. In order to solve these problems efficiently, we develop a novel active-set algorithm that takes into account past active constraints to accelerate the resolution of unresolved contacts. We put to a test the developed collision procedure with diverse scenarios involving static and dynamic friction, sharp objects, and complex-topology folding sequences. Finally, we perform an experimental validation of the collision model by comparing simulations with recordings of real textiles as given by a Motion Capture System. The results are very accurate, having errors around 1 cm for DIN A2 textiles (42 x 59.4 cm) even in difficult scenarios involving fast and strong hits with a rigid object. In this work, we present a novel collision model for inextensible textiles and validate it experimentally through a comparison with real textiles as recorded by a Motion Capture System. In the figure we can see four frames comparing the recorded hitting with a stick of a DIN A2 (42 x 59.4 cm) polyester sheet (left) with its inextensible simulation (right); its average error being 1.44 cm. The recordings are obtained by attaching 20 reflective markers of diameter 3 mm and weight of 0.013 g to the real textile and following their trajectory. On the bottom, we show a full plot of the mean absolute error of the position of each marker with respect to its simulation and with yellow lines we highlight the moments in which the object is in contact with the cloth. Notice that the biggest errors appear not during the hits but just after because of aerodynamic effects. The above simulations, with a 7 × 9 mesh, are two times faster than real-time. Our custom active-set solver is three times faster than a standard interior-point method using the same mesh resolution. • We develop a cloth collision model which results in a coupled resolution of friction, inextensibility, and contact forces. • Self-collisions are modeled in a way that allows considering cloth's thickness without introducing unwanted oscillations. • An active-set solver for the system's integration is developed, which can start from any non-necessarily feasible point. • An empirical validation is performed, with scenarios involving high-friction surfaces and strong hits with a stick. [ABSTRACT FROM AUTHOR]

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund's filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications. [ABSTRACT FROM AUTHOR]

In order to address stringent standards, energy efficiency objectives or also cost reduction imperatives, the optimal design of complex industrial structures is an important concern. In this context, parametric optimization offers a powerful tool for engineers. Taking into account nonlinear behavior in the models allows performing high-fidelity numerical simulations and thus reducing safety margins. However, in vibration dynamics, the use of classical global optimization methods on industrial-scale structures with nonlinearities is not affordable due to too many required solver calls to localize the optimum. This work proposes an approach to achieve global constrained optimization of structures with local nonlinearities in vibration. The strategy is based on a Bayesian Optimization process relying on two tools: (i) a Gaussian Process as a surrogate model and (ii) a dedicated nonlinear mechanical solver based on the Harmonic Balance Method. These two tools are presented in detail. Their performance and characteristics are presented and analyzed on academic and industrial-scale examples. The whole strategy is finally applied on a Duffing oscillator without optimization's constraint and a gantry crane to illustrate the efficiency on constrained optimization. In addition, many discussions are made relative to the number of initial sample points. The results show that the proposed approach is able to find the global optimum with a limited number of solver calls, demonstrating its ability to be integrated into an actual industrial design process. [ABSTRACT FROM AUTHOR]

We analyzed a special class of graph traversal problems, where the distances are stochastic, and the agent is restricted to take a limited range in one go. We showed that both constrained shortest Hamiltonian pathfinding problems and disassembly line balancing problems belong to the class of constrained shortest pathfinding problems, which can be represented as mixed-integer optimization problems. Reinforcement learning (RL) methods have proven their efficiency in multiple complex problems. However, researchers concluded that the learning time increases radically by growing the state- and action spaces. In continuous cases, approximation techniques are used, but these methods have several limitations in mixed-integer searching spaces. We present the Q-table compression method as a multistep method with dimension reduction, state fusion, and space compression techniques that project a mixed-integer optimization problem into a discrete one. The RL agent is then trained using an extended Q-value-based method to deliver a human-interpretable model for optimal action selection. Our approach was tested in selected constrained stochastic graph traversal use cases, and comparative results are shown to the simple grid-based discretization method. [ABSTRACT FROM AUTHOR]

In this contribution, a new approach to design interval observer for continuous-time linear systems is introduced. First, a more general structure than the classical Luenberger observer is proposed and extended to the interval case based on an explicit set integration method. Then, to obtain tight state enclosures, the computation of the design matrices involved in this new structure is formulated as a nonlinear constrained optimisation problem. In addition, using the symmetric property of interval vectors, a less complex form of the proposed interval observer is presented. On the other hand, compared to the conventional interval observers, no preserving order property on the dynamics of the estimation error is required to apply the introduced method. A numerical case study example is considered to illustrate the effectiveness of the proposed method and to compare its performance to that of a former method. [ABSTRACT FROM AUTHOR]

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1–35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart. [ABSTRACT FROM AUTHOR]

We propose logarithmic-barrier decomposition-based interior-point algorithms for solving two-stage stochastic quadratically constrained convex quadratic programming problems in a Hilbert space. We prove the polynomial complexity of the proposed algorithms, and show that this complexity is independent on the choice of the Hilbert space, and hence it coincides with the best-known complexity estimates in the finite-dimensional case. We also apply our results on a concrete example from the stochastic control theory. [ABSTRACT FROM AUTHOR]

Many practical problems can be classified as constrained multi-objective optimization problems. Although various methods have been proposed for solving constrained multi-objective optimization problems, there is still a lack of research considering the integration of multiple constraint handling techniques. Given this, this paper combines the objective and constraint separation method with the multi-operator method, proposing a population feasibility state guided autonomous constrained evolutionary optimization method. This method first defines the feasibility state of the population based on both feasibility and ε feasibility of the solutions. Subsequently, a reinforcement learning model is employed to construct a mapping model between the population state and reproduction operators. Finally, based on the real-time population state, the mapping model is utilized to recommend the promising reproduction operator for the next generation. This approach demonstrates significant performance improvement for ε constrained mechanisms in constrained multi-objective optimization algorithms, and shows considerable advantages in comparison with state-of-the-art constrained multi-objective optimization algorithms. [ABSTRACT FROM AUTHOR]

The dynamic economic dispatch (DED) problem is a typical complex constrained optimization problem with non-smooth, nonlinear, and nonconvex characteristics, especially considering practical situations such as valve point effects and transmission losses, and its objective is to minimize the total fuel costs and total carbon emissions of generating units during the dispatch cycle while satisfying a series of equality and inequality constraints. For the challenging DED problem, a model of a dynamic economic dispatch problem considering fuel costs is first established, and then an improved grey wolf optimization algorithm (IGWO) is proposed, in which the exploitation and exploration capability of the original grey wolf optimization algorithm (GWO) is enhanced by initializing the population with a chaotic algorithm and introducing a nonlinear convergence factor to improve weights. Furthermore, a simple and effective constraint-handling method is proposed for the infeasible solutions. The performance of the IGWO is tested with eight benchmark functions selected and compared with other commonly used algorithms. Finally, the IGWO is utilized for three different scales of DED cases, and compared with existing methods in the literature. The results show that the proposed IGWO has a faster convergence rate and better global optimization capabilities, and effectively reduces the fuel costs of the units, thus proving the effectiveness of IGWO. [ABSTRACT FROM AUTHOR]

The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems, in which the objective function is stochastic and the constraints are deterministic. The method proposed in this paper is a proximal gradient method that can also be applied to the composite optimization problem min |$f(x) + h(x)$|⁠ , where |$f$| is stochastic and |$h$| is convex (but not necessarily differentiable). Adaptive sampling methods employ a mechanism for gradually improving the quality of the gradient approximation so as to keep computational cost to a minimum. The mechanism commonly employed in unconstrained optimization is no longer reliable in the constrained or composite optimization settings, because it is based on pointwise decisions that cannot correctly predict the quality of the proximal gradient step. The method proposed in this paper measures the result of a complete step to determine if the gradient approximation is accurate enough; otherwise, a more accurate gradient is generated and a new step is computed. Convergence results are established both for strongly convex and general convex |$f$|⁠. Numerical experiments are presented to illustrate the practical behavior of the method. [ABSTRACT FROM AUTHOR]

We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal optimization method as a nonconvex but practically tractable quadratically constrained quadratic optimization problem and solves it to certifiable global optimality using a customized branch-and-bound algorithm. By directly confronting the nonconvexity, BnB-PEP offers significantly more flexibility and removes the many limitations of the prior methodologies. Our customized branch-and-bound algorithm, through exploiting specific problem structures, outperforms the latest off-the-shelf implementations by orders of magnitude, accelerating the solution time from hours to seconds and weeks to minutes. We apply BnB-PEP to several setups for which the prior methodologies do not apply and obtain methods with bounds that improve upon prior state-of-the-art results. Finally, we use the BnB-PEP methodology to find proofs with potential function structures, thereby systematically generating analytical convergence proofs. [ABSTRACT FROM AUTHOR]

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme. [ABSTRACT FROM AUTHOR]

A nonconvex distributed optimization problem involving nonconvex objective functions and inequality constraints within an undirected multi-agent network is considered. Each agent communicates with its neighbors while only obtaining its individual local information (i.e. its constraint and objective function information). To overcome the challenge caused by the nonconvexity of the objective function, a collective neurodynamic penalty approach in the framework of particle swarm optimization is proposed. The state solution convergence of every neurodynamic penalty approach is directed towards the critical point ensemble of the nonconvex distributed optimization problem. Furthermore, employing their individual neurodynamic models, each neural network conducts accurate local searches within constraints. Through the utilization of both locally best-known solution information and globally best-known solution information, along with the incremental enhancement of solution quality through iterations, the globally optimal solution for a nonconvex distributed optimization problem can be found. Simulations and an application are presented to demonstrate the effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

Drug discovery and development constitute a laborious and costly undertaking. The success of a drug hinges not only good efficacy but also acceptable absorption, distribution, metabolism, elimination, and toxicity (ADMET) properties. Overall, up to 50% of drug development failures have been contributed from undesirable ADMET profiles. As a multiple parameter objective, the optimization of the ADMET properties is extremely challenging owing to the vast chemical space and limited human expert knowledge. In this study, a freely available platform called Chemical Molecular Optimization, Representation and Translation (ChemMORT) is developed for the optimization of multiple ADMET endpoints without the loss of potency (https://cadd.nscc-tj.cn/deploy/chemmort/). ChemMORT contains three modules: Simplified Molecular Input Line Entry System (SMILES) Encoder, Descriptor Decoder and Molecular Optimizer. The SMILES Encoder can generate the molecular representation with a 512-dimensional vector, and the Descriptor Decoder is able to translate the above representation to the corresponding molecular structure with high accuracy. Based on reversible molecular representation and particle swarm optimization strategy, the Molecular Optimizer can be used to effectively optimize undesirable ADMET properties without the loss of bioactivity, which essentially accomplishes the design of inverse QSAR. The constrained multi-objective optimization of the poly (ADP-ribose) polymerase-1 inhibitor is provided as the case to explore the utility of ChemMORT. [ABSTRACT FROM AUTHOR]

The paper is devoted to the theoretical and numerical analysis of the two-step method, constructed as a modification of Polyak's heavy ball method with the inclusion of an additional momentum parameter. For the quadratic case, the convergence conditions are obtained with the use of the first Lyapunov method. For the non-quadratic case, sufficiently smooth strongly convex functions are obtained, and these conditions guarantee local convergence.An approach to finding optimal parameter values based on the solution of a constrained optimization problem is proposed. The effect of an additional parameter on the convergence rate is analyzed. With the use of an ordinary differential equation, equivalent to the method, the damping effect of this parameter on the oscillations, which is typical for the non-monotonic convergence of the heavy ball method, is demonstrated. In different numerical examples for non-quadratic convex and non-convex test functions and machine learning problems (regularized smoothed elastic net regression, logistic regression, and recurrent neural network training), the positive influence of an additional parameter value on the convergence process is demonstrated. [ABSTRACT FROM AUTHOR]

This paper focuses on the cardinality constrained mean-variance portfolio optimization, in which only a small number of assets are invested. We first treat the covariance matrix of asset returns as a diagonal matrix with a special matrix processing technique. Using the dual theory, we formulate the lower bound problem of the original problem as a max-min optimization. For the inner minimization problem with the cardinality constraint, we obtain its analytical solution for the portfolio weights. Then, the lower bound problem turns out to be a simple concave optimization with respect to the Lagrangian multipliers. Thus, the interval split method and the supergradient method are developed to solve it. Based on the precise lower bound, the depth-first branch and bound method are designed to find the global optimal investment selection strategy. Compared with other lower bounds and the current popular mixed integer programming solvers, such as CPLEX and SCIP, the numerical experiments show that our method has a high searching efficiency. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12101317, 12271071, and 11991024], the Natural Science Foundation of Jiangsu Province [Grant BK20200819], the Team Project of Innovation Leading Talent in Chongqing [Grant CQYC20210309536], the Contract System Project of Chongqing Talent Plan [Grant cstc2022ycjh-bgzxm0147], and the Philosophy and Social Science Fund of Education Department of Jiangsu Province [Grant 2020SJA0168]. K.F.C. Yiu is supported in part by the Research Grants Council of Hong Hong [Grant PolyU 15223419], the Hong Kong Polytechnic University [Grants 4-ZZPT and 1-WZ0E], and the Research Centre for Quantitative Finance [Grant 1-CE03]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0344) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0344). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work of A. Sharma on DiffOpt.jl was funded by the Google Summer of Code program through NumFocus. M. Besançon was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research [Grant 05M14ZAM, 05M20ZBM]. J. Dias Garcia was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. B. Legat was supported by a BAEF Postdoctoral Fellowship, the NSF [Grant OAC-1835443], and the ERC Adv. [Grant 885682]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0283), as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0283). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

For an unbalanced cooperative game, its grand coalition can be stabilized by some instruments, such as subsidization and penalization, that impose new cost terms to certain coalitions. In this paper, we study an alternative instrument, referred to as cost adjustment, that does not need to impose any new coalition-specific cost terms. Specifically, our approach is to adjust existing cost coefficients of the game under which (i) the game becomes balanced so that the grand coalition becomes stable, (ii) a desired way of cooperation is optimal for the grand coalition to adopt, and (iii) the total cost to be shared by the grand coalition is within a prescribed range. Focusing on a broad class of cooperative games, known as integer minimization games, we formulate the problem on how to optimize the cost adjustment as a constrained inverse optimization problem. We prove NP -hardness and derive easy-to-check feasibility conditions for the problem. Based on two linear programming reformulations, we develop two solution algorithms. One is a cutting-plane algorithm, which runs in polynomial time when the corresponding separation problem is polynomial time solvable. The other needs to explicitly derive all the inequalities of a linear program, which runs in polynomial time when the linear program contains only a polynomial number of inequalities. We apply our models and solution algorithms to two typical unbalanced games, including a weighted matching game and an uncapacitated facility location game, showing that their optimal cost adjustments can be obtained in polynomial time. History: Accepted by Area Editor Andrea Lodi for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72022018 and 72091210]; the Research Grants Council of the Hong Kong SAR, China [Grant 16210020]; Hong Kong Polytechnic University [Grant P0032007]; and the Youth Innovation Promotion Association, Chinese Academy of Sciences [Grant 2021454]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0268. [ABSTRACT FROM AUTHOR]

This paper introduces the Botox Optimization Algorithm (BOA), a novel metaheuristic inspired by the Botox operation mechanism. The algorithm is designed to address optimization problems, utilizing a human-based approach. Taking cues from Botox procedures, where defects are targeted and treated to enhance beauty, the BOA is formulated and mathematically modeled. Evaluation on the CEC 2017 test suite showcases the BOA's ability to balance exploration and exploitation, delivering competitive solutions. Comparative analysis against twelve well-known metaheuristic algorithms demonstrates the BOA's superior performance across various benchmark functions, with statistically significant advantages. Moreover, application to constrained optimization problems from the CEC 2011 test suite highlights the BOA's effectiveness in real-world optimization tasks. [ABSTRACT FROM AUTHOR]