Search

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]

As a nature-inspired metaheuristic method, the firefly algorithm (FA) arises more attentions in academic and engineering fields. However, too much attraction in FA's global attraction model leads to low computational efficiency, and the stochastic model with fixed randomization parameter is hard to balance the exploitation and exploration of the algorithm. Thus, FA still needs improvement to deal with complex engineering problems. An integrated firefly algorithm (IFA) that combines two novel attractive models with a new stochastic model is proposed to improve the standard FA. Firstly, the attractive model and stochastic model of standard FA are investigated through theoretical analysis and numerical experiments. And the factors that affect the computational efficiency and accuracy of FA are revealed. Based on the analysis results, two new fitness-based update formulas for attractiveness parameter are constructed to avoid the invalidation. The proposed virtual attractive model and global best attractive model can reduce the computation complexity and enhance the exploitation ability. Moreover, an adaptive strategy is presented for the stochastic model to achieve a better balance between exploitation and exploration. The nonlinearly decreased model for the update of parameter α can adjust the population diversity through the iteration and ensure the convergence. Additionally, an adaptive penalty function method is developed to handle the constraints effectively. Then, the initial parameters are tested, and the best initial parameters corresponding to the optimal performance of IFA are obtained. The proposed algorithm is evaluated by CEC2015 hybrid composition and a set of classical functions. The numerical experimental results show that the proposed techniques can enhance the solution accuracy and accelerate the convergence speed. Finally, IFA and other metaheuristic algorithms are applied to solve five engineering design optimization problems with mixed variables and multiple constraint conditions. The results indicate that IFA with adaptive penalty function needs fewer fitness evaluations and costs less computational time to obtain the optimal solutions. Furthermore, it exhibits better accuracy and robustness than other algorithms. [ABSTRACT FROM AUTHOR]

We consider a portfolio optimisation problem for a utility-maximising investor who faces convex constraints on his portfolio allocation in Heston's stochastic volatility model. We apply existing duality methods to obtain a closed-form expression for the optimal portfolio allocation. In doing so, we observe that allocation constraints impact the optimal constrained portfolio allocation in a fundamentally different way in Heston's stochastic volatility model than in the Black Scholes model. In particular, the optimal constrained portfolio may be different from the naive 'capped' portfolio, which caps off the optimal unconstrained portfolio at the boundaries of the constraints. Despite this difference, we illustrate by way of a numerical analysis that in most realistic scenarios the capped portfolio leads to slim annual wealth equivalent losses compared to the optimal constrained portfolio. During a financial crisis, however, a capped solution might lead to compelling annual wealth equivalent losses. [ABSTRACT FROM AUTHOR]

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided. [ABSTRACT FROM AUTHOR]

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence. [ABSTRACT FROM AUTHOR]

Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration. [ABSTRACT FROM AUTHOR]

A new subspace minimization conjugate gradient algorithm with a nonmonotone Wolfe line search is proposed and analyzed. In the scheme, we propose two choices of the search direction by minimizing a quadratic approximation of the objective function in special subspaces, and state criterions on how to choose the direction. Under given conditions, we obtain the significant conclusion that each choice of the direction satisfies the sufficient descent property. Based on the idea on how the function is close to a quadratic function, a new strategy for choosing the initial stepsize is presented for the line search. With the used nonmonotone Wolfe line search, we prove the global convergence of the proposed method for general nonlinear functions under mild assumptions. Numerical comparisons are given with well-known CGOPT and CG_DESCENT and show that the proposed algorithm is very promising. [ABSTRACT FROM AUTHOR]

In this paper, based on a new smoothing function, the general box constrained variational inequalities are solved by a smoothing Newton algorithm with a nonmonotone line search. The proposed algorithm is proved to be globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Numerical methods for computing plausibility and belief distributions of consequences of a subjective model are considered. More precisely, related constrained optimization problems are studied. Error estimates of the proposed algorithms are obtained. Techniques for taking into account the information about the consequence available to the researcher for improving the accuracy of computations are discussed. [ABSTRACT FROM AUTHOR]

For the structured systems of linear equations arising from the Galerkin finite element discretizations of elliptic PDE-constrained optimization problems, some preconditioners are proposed to accelerate the convergence rate of Krylov subspace methods such as GMRES for both cases of the Tikhonov parameter β not very small (equal or greater than 1e−6) and sufficiently small (less than 1e−6), respectively. We derive the explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices. Numerical results show that the corresponding preconditioned GMRES methods perform and match well with the theoretical results. [ABSTRACT FROM AUTHOR]

We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a sequence of representative models of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide the parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy. [ABSTRACT FROM PUBLISHER]

In this article, we focus on mobile wellness and health-related applications from the perspective of the level of imprecision present in the data used in the recommendation systems. We propose a general fuzzy optimization model based on chanced constrained optimization to design recommendation systems that can take into consideration (i) the imprecision in the data and (ii) the imprecision by which one can estimate the effect of a recommendation on the user of the system. Our proposal is one of the first to use fuzzy optimization models in health-related decision making problems and the first to define a chance constrained optimization problem for interval-valued fuzzy numbers. The proposed approach identifies a set of actions to be taken by the users in order to optimize general health-related and/or wellness condition of the user from various perspectives. The model is illustrated through the example of walking speed optimization, with an additional numerical experiment offering a comparison with traditional methods. [ABSTRACT FROM AUTHOR]

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions, and it allows the treatment of inequality constraints with infinitedimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global optimality, and KKT conditions. Some numerical results are given to illustrate the practical viability of the method. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical investigation of nonlinear optimal control problems with multiple delays in which the state trajectory and control input are subject to mixed state-control constraints. A direct approach based on a hybrid of block-pulse functions and Lagrange interpolation is proposed. The constrained optimal control problem is first reformulated as an unconstrained optimization one using a penalty function technique. The resulting optimization problem is then solved by means of the Lagrange multipliers procedure. The proposed framework is an extension and also a modification of the conventional Lagrange interpolation. Combining block-pulse functions and Lagrange interpolation allows one to simultaneously make use the advantages of the two mentioned bases. The operational matrices of delay and derivative associated with the hybrid functions are presented. An upper error bound for the proposed hybrid functions with respect to the maximum norm is obtained. Simulation studies are provided to verify the validity and reliability of the developed procedure. [ABSTRACT FROM AUTHOR]

In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation . Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results. [ABSTRACT FROM AUTHOR]

In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

This article addresses one of the major constraints imposed by additive manufacturing processes on shape optimization problems – that of overhangs, i.e. large regions hanging over void without sufficient support from the lower structure. After revisiting the ‘classical’ geometric criteria used in the literature, based on the angle between the structural boundary and the build direction, we propose a new mechanical constraint functional, which mimics the layer by layer construction process featured by additive manufacturing technologies, and thereby appeals to the physical origin of the difficulties caused by overhangs. This constraint, as well as some variants, is precisely defined; their shape derivatives are computed in the sense of Hadamard's method, and numerical strategies are extensively discussed, in two and three space dimensions, to efficiently deal with the appearance of overhang features in the course of shape optimization processes. [ABSTRACT FROM AUTHOR]

The design of a propeller for a high-speed craft is addressed by using a multi-objective numerical optimization approach. By combining a fast and reliable Boundary Elements Method (BEM), a viscous flow solver based on the RANSE approximation, a parametric 3D description of the blade and a genetic algorithm, the new propeller shape is designed to improve the propulsive efficiency, reduce the cavitation extension, increase the cavitation inception speed and maximize, at the same time, the ship speed. Rather than by constraining the propeller delivered thrust, indeed, the proposed procedure works together with an engine-propeller matching algorithm that, each time a new propeller is defined, identifies the achievable maximum ship speed and the resulting engine functioning point that turn in additional goals for the multi-objective optimization. A set of optimal propellers, obtained through the design by optimization based on potential flow calculations (via the Boundary Elements Method), are selected for additional viscous analyses (RANSE calculations) in order to further validate the results of the BEM calculations and provide a deeper insight into the complex flow fields of high speed propellers. Among this subset of optimal configurations, a final geometry is selected to verify the reliability of the design procedure by means of dedicated cavitation tunnel tests and full-scale measurements on a high-speed craft provided by Azimut|Benetti. [ABSTRACT FROM AUTHOR]

In the context of change-point detection, addressed by Total Variation minimization strategies, an efficient on-the-fly algorithm has been designed leading to exact solutions for univariate data. In this contribution, an extension of such an on-the-fly strategy to multivariate data is investigated. The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker conditions on the dual problem. Showing that the non-local nature of the multivariate setting precludes to obtain an exact on-the-fly solution, we devise an on-the-fly algorithm delivering an approximate solution, whose quality is controlled by a practitioner-tunable parameter, acting as a trade-off between quality and computational cost. Performance assessment shows that high quality solutions are obtained on-the-fly while benefiting of computational costs several orders of magnitude lower than standard iterative procedures. The proposed algorithm thus provides practitioners with an efficient multivariate change-point detection on-the-fly procedure. [ABSTRACT FROM PUBLISHER]

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented. [ABSTRACT FROM AUTHOR]

This paper presents a new powerful nature-inspired method named Virus Colony Search (VCS). VCS simulates diffusion and infection strategies for the host cells adopted by virus to survive and propagate in the cell environment. With the strategies, the individual in the new algorithm explores and exploits the search space more efficiently. To verify the performance of our VCS, both the unconstrained classic and CEC2014 modern benchmark functions, and constrained engineering design optimization problems are employed. The experimental results, considering both convergence and accuracy simultaneously, demonstrate the effectiveness of VCS for global numerical and engineering optimization problems. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of finding a solution of a nonsmooth constrained (and not necessarily square) system of equations. We first reformulate the original problem as an equivalent system of equations with nonnegative constraints, and then present a smoothing projected Levenberg-Marquardt type algorithm to solve the reformulated system, which solves a strictly convex quadratic program at each iteration. We show that this algorithm not only converges globally, but also converges locally superlinearly under an error bound assumption that is much weaker than the standard nonsingularity condition. Some numerical results for the presented algorithm indicate that the algorithm works quite well in practice. [ABSTRACT FROM PUBLISHER]

Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper [Banihashemi and Kaya (2013)] suggests that the Inexact Restoration approach can be competitive with well-established nonlinear programming solvers when applied to certain control problems without any problem-oriented procedure for restoring feasibility. This result motivated us to revisit the idea of designing general-purpose Inexact Restoration methods, especially for large-scale problems. In this paper we introduce affordable algorithms of Inexact Restoration type for solving arbitrary nonlinear programming problems and we perform the first experiments that aim to assess their reliability. Initially, we define a purely local Inexact Restoration algorithm with quadratic convergence. Then, we modify the local algorithm in order to increase the chances of success of both the restoration and the optimization phase. This hybrid algorithm is intermediate between the local algorithm and a globally convergent one for which, under suitable assumptions, convergence to KKT points can be proved. [ABSTRACT FROM AUTHOR]

This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network. [ABSTRACT FROM AUTHOR]

In this paper the method of penalized high order Legendre polynomials and specific designs of experiments for model building on the basis of numerical or physical experiments is proposed. The generalized thin-plate energy functional is used for penalization of the least square functional. The optimal choice of smoothing parameter (penalization coefficient) is implemented using the cross-validation method. Special axial-symmetrical and 90 degree rotational symmetrical D-optimal experimental designs are obtained using the direct constrained optimization method. The method was tested for known optimization test problems with 2-5 variables and showed prediction accuracy comparable with kriging. [ABSTRACT FROM AUTHOR]

The paper presents a constrained optimization procedure (COP) for the dynamic analysis of hybrid base isolation systems under earthquake excitation. After a description of the hybrid system considered, the mechanical model used for its representation is introduced, along with the governing equations. Mid-point central difference time-discretization is used to cast the computations in each time increment as a quadratic optimization problem with non-linear constraints. Numerical applications illustrate the accuracy and robustness of the formulation and highlight some typical performance characteristics of hybrid base isolation systems. [ABSTRACT FROM AUTHOR]

Seeker optimization algorithm is one of the recent swarm intelligence metaheuristics for hard optimization problems. It is based on the human group search behavior and it was successfully applied to various numerical optimization problems. While the seeker optimization algorithm was proven to be successful for different specific problems, it was not properly tested on a wide set of benchmark functions. Our testing on the standard well-known set of benchmark functions shows that the seeker optimization algorithm has serious problems with some types of functions. In this paper we introduced modifications to the seeker optimization algorithm to control exploitation/exploration balance and hybridized it with elements of the firefly algorithm that improved its exploitation capabilities. The firefly algorithm alone also exhibits deficiencies. Our proposed modified and hybridized seeker optimization algorithm not only overcame shortcomings of the original algorithms, but also outperformed other state-of-the-art swarm intelligence algorithms. [ABSTRACT FROM AUTHOR]

We give an existence result to a class of evolutionary quasi-variational inequalities with adaptive set of feasible solutions, where the adaptivity is modeled by solution-dependent equality constraints. A fundamental role will be played by the concept of Mosco convergence related to set-valued applications. Finally, we apply our achievements to the dynamic multiclass network equilibrium problem and provide a numerical example. [ABSTRACT FROM AUTHOR]

This paper presents a new dissipativity-based decentralized model predictive control strategy for networks of linear systems suffering from a bounded coupling delay. The notion of delay-robust dissipativity is introduced and applied to the development of interconnection stability conditions. The dissipation inequality of system trajectories is converted into a prognostic stability constraint for the optimization problem of model predictive control to guarantee the system stability. A recursive feasibility condition is derived for the constrained optimization problem, which is formulated in a semi-definite program. A numerical example of an interconnected three-unit process system is provided for illustrations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study an efficient tridiagonal preconditioner, based on the directional differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experiments. [Copyright &y& Elsevier]

The article considers optimization of mixed constraints for a controlled system that describes countrylevel economic growth driven by technological progress. An algorithm is proposed, reducing this problem to an equivalent general optimization problem in a normed space, which in turn is solved by an iterative method based on N. N. Krasovskii's extremal shift method. Calculation results are reported for the economy of Japan in the second half of the twentieth century. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new meta-heuristic called Grey Wolf Optimizer inspired by grey wolves is proposed. [•] The GWO algorithm is benchmarked on 29 well-known test functions. [•] The results on the unimodal functions show the superior exploitation of GWO. [•] The exploration ability of GWO is confirmed by the results on multimodal functions. [•] The results on semi-real and real problems confirm the performance of GWO in practice. [ABSTRACT FROM AUTHOR]

The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization. The feasibility restoration phase, which is always used in the traditional filter method, is not needed. Under mild conditions, global convergence and local superlinear convergence rates are obtained. Numerical results demonstrate that the new algorithm is effective. [ABSTRACT FROM AUTHOR]

We analyse the problem of constrained minimization of the real quadratic functional, subject to the inconsistent system of linear equations, whereis a positive definite or positive semidefinite matrix. Both cases are analysed separately, and respective relationships have been established between the solution of the original problem and the Drazin-inverse solution of the equation. In the special case whenis a positive definite and, we show that the solution of the problem can be represented as a particular-inverse solution. [ABSTRACT FROM AUTHOR]

This article develops two new algorithms for constrained expensive black-box optimization that use radial basis function surrogates for the objective and constraint functions. These algorithms are called COBRA and Extended ConstrLMSRBF and, unlike previous surrogate-based approaches, they can be used for high-dimensional problems where all initial points are infeasible. They both follow a two-phase approach where the first phase finds a feasible point while the second phase improves this feasible point. COBRA and Extended ConstrLMSRBF are compared with alternative methods on 20 test problems and on the MOPTA08 benchmark automotive problem (D.R. Jones, Presented at MOPTA 2008), which has 124 decision variables and 68 black-box inequality constraints. The alternatives include a sequential penalty derivative-free algorithm, a direct search method with kriging surrogates, and two multistart methods. Numerical results show that COBRA algorithms are competitive with Extended ConstrLMSRBF and they generally outperform the alternatives on the MOPTA08 problem and most of the test problems. [ABSTRACT FROM AUTHOR]

A novel filled function method is suggested for solving box-constrained systems of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a novel filled function with one parameter is proposed for solving the converted global optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed novel filled function for solving systems of nonlinear equations is presented. The objective function value can be reduced by quarter in each iteration of our algorithm. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [ABSTRACT FROM AUTHOR]

A practical algorithm for solving large-scale box-constrained optimization problems is developed, analyzed, and tested. In the proposed algorithm, an identification strategy is involved to estimate the active set at per-iteration. The components of inactive variables are determined by the steepest descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method--L-BFGS-B. [ABSTRACT FROM AUTHOR]

Abstract: A new line search method is introduced for solving nonlinear equality constrained optimization problems. It does not use any penalty function or a filter. At each iteration, the trial step is determined such that either the value of the objective function or the measure of the constraint violation is sufficiently reduced. Under usual assumptions, it is shown that every limit point of the sequence of iterates generated by the algorithm is feasible, and there exists at least one limit point that is a stationary point for the problem. A simple modification of the algorithm by introducing second order correction steps is presented. It is shown that the modified method does not suffer from the Maratos’ effect, so that it converges superlinearly. The preliminary numerical results are reported. [Copyright &y& Elsevier]

In this paper, a new adaptive grouping differential evolution (AGDE) algorithm is proposed to improve the optimization performance by implementing a prediction strategy of the constraints for constrained optimization problems. It is unnecessary to calculate the constraint values when dealing with the constraints in this method. The constraints are handled after a simple prediction according to the Lipschitz condition. When the constraints are very complex, the load arisen from the calculation of the constraint values is reduced dramatically and the feasibility of the solutions remains with great probability. In AGDE algorithm, the population is dynamically grouped to three subpopulations with respective newly-designed mutation strategy. Meanwhile, the mutation factor and crossover probability are adopted associated with the evolutionary process according to the information of the entire population. Both of the above improvements not only increase the diversity of population and speed up the convergence, but also reduce the complexity of the parameter selection. Four sets of comparative experiments are carried out to evaluate the feasibility and effectiveness of the proposed method that deals with the constraints. [ABSTRACT FROM AUTHOR]

Abstract: The linear least squares (LLS) technique is widely used in time-difference-of-arrival based positioning because of its computational efficiency. Two-step weighted least squares (2WLS) and constrained weighted least squares (CWLS) algorithms are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this paper, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approach. The performance of the proposed method is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate its localization accuracy by comparing with the existing 2WLS and CWLS algorithms as well as the Cramér–Rao lower bound. [Copyright &y& Elsevier]

This article presents the DYCORS (DYnamic COordinate search using Response Surface models) framework for surrogate-based optimization of HEB (High-dimensional, Expensive, and Black-box) functions that incorporates an idea from the DDS (Dynamically Dimensioned Search) algorithm. The iterate is selected from random trial solutions obtained by perturbing only a subset of the coordinates of the current best solution. Moreover, the probability of perturbing a coordinate decreases as the algorithm reaches the computational budget. Two DYCORS algorithms that use RBF (Radial Basis Function) surrogates are developed: DYCORS-LMSRBF is a modification of the LMSRBF algorithm while DYCORS-DDSRBF is an RBF-assisted DDS. Numerical results on a 14-D watershed calibration problem and on eleven 30-D and 200-D test problems show that DYCORS algorithms are generally better than EGO, DDS, LMSRBF, MADS with kriging, SQP, an RBF-assisted evolution strategy, and a genetic algorithm. Hence, DYCORS is a promising approach for watershed calibration and for HEB optimization. [ABSTRACT FROM AUTHOR]

Abstract: Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on the quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limited-memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. The resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of the presented methods is established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems. [Copyright &y& Elsevier]

Abstract: A simple three-term conjugate gradient algorithm which satisfies both the descent condition and the conjugacy condition is presented. This algorithm is a modification of the Hestenes and Stiefel algorithm (Hestenes and Stiefel, 1952) [10], or that of Hager and Zhang (Hager and Zhang, 2005) [23] in such a way that the search direction is descent and it satisfies the conjugacy condition. These properties are independent of the line search. Also, the algorithm could be considered as a modification of the memoryless BFGS quasi-Newton method. The new approximation of the minimum is obtained by the general Wolfe line search, now using a standard acceleration technique developed by Andrei (2009) [27]. For uniformly convex functions, under standard assumptions, the global convergence of the algorithm is proved. Numerical comparisons of the suggested three-term conjugate gradient algorithm versus six other three-term conjugate gradient algorithms, using a set of 750 unconstrained optimization problems, show that all these computational schemes have similar performances, the suggested one being slightly faster and more robust. The proposed three-term conjugate gradient algorithm substantially outperforms the well-known Hestenes and Stiefel conjugate gradient algorithm, as well as the more elaborate CG_DESCENT algorithm. Using five applications from the MINPACK-2 test problem collection (Averick et al., 1992) [25], with variables, we show that the suggested three-term conjugate gradient algorithm is the top performer versus CG_DESCENT. [Copyright &y& Elsevier]