Search

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]

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]

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]

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]

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]

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]

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]

Abstract: We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd–Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato’s effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded cylindrical shells subjected to mechanical loadings. Eight types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded cylindrical shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out. [Copyright &y& Elsevier]

Abstract: In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced. [Copyright &y& Elsevier]

Abstract: A higher order numerical discretization technique based on Minimum Sobolev Norm (MSN) interpolation was introduced in our previous work. In this article, the discretization technique is presented as a tool to solve two hard classes of PDEs, namely, the exterior Laplace problem and the biharmonic problem. The exterior Laplace problem is compactified and the resultant near singular PDE is solved using this technique. This finite difference type method is then used to discretize and solve biharmonic type PDEs. A simple book keeping trick of using Ghost points is used to obtain a perfectly constrained discrete system. Numerical results such as discretization error, condition number estimate, and solution error are presented. For both classes of PDEs, variable coefficient examples on complicated geometries and irregular grids are considered. The method is seen to have high order of convergence in all these cases through numerical evidence. Perhaps for the first time, such a systematic higher order procedure for irregular grids and variable coefficient cases is now available. Though not discussed in the paper, the idea seems to be easily generalizable to finite element type techniques as well. [Copyright &y& Elsevier]

Abstract: Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a descent search direction. On the other hand, Hager and Zhang (2005) proposed another conjugate gradient method which always generates a descent search direction. In this paper, combining Dai–Liao’s idea and Hager–Zhang’s idea, we propose conjugate gradient methods based on secant conditions that generate descent search directions. In addition, we prove global convergence properties of the proposed methods. Finally, preliminary numerical results are given. [Copyright &y& Elsevier]

Abstract: The generation of priority vectors from pairwise comparison matrices is an essential part of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (REV) which was proposed by Saaty. Despite its popularity some shortcomings of the REV have been reported in literature. Among the alternative approaches one can find the statistical estimation techniques, methods founded on constrained optimization models and models based on fuzzy description of decision maker preferences. In this paper new optimization techniques for deriving priority weights are introduced. In the proposed approach, the constrained optimization models are based on the same idea which underlies the REV. The properties of the resulting prioritization techniques are studied via computer simulations. This study demonstrates that the new methods perform very well in comparison with other popular techniques known from literature. What is especially important, the new approach provides the decision maker with a meaningful index that can be used to measure consistency of his/her judgments. The new index is closely related to the well-known Saaty’s consistency index CI, but in difference to the latter, it can be applied to both reciprocal as well as nonreciprocal comparison matrices. Hence the new index can be considered as a natural extension of the CI to all types of matrices. Some additional advantages resulting from the new approach are discussed and illustrated by numerical examples. [Copyright &y& Elsevier]

Abstract: A new sequential quadratic programming (SQP) method for nonlinear inequality constrained optimization is proposed. The aim of this paper is to promote global convergence for SQP methods using a flexible step acceptance strategy which combines merit functions and filter techniques. Global convergence is proved under some reasonable assumptions and preliminary numerical results are reported. [Copyright &y& Elsevier]

For solving large-scale unconstrained minimization problems, the nonlinear conjugate gradient method is welcome due to its simplicity, low storage, efficiency and nice convergence properties. Among all the methods in the framework, the conjugate gradient descent algorithm — CG_DESCENT is very popular, in which the generated directions descend automatically, and this nice property is independent of any line search used. In this paper, we generalize CG_DESCENT with two Barzilai–Borwein steplength reused cyclically. We show that the resulting algorithm owns attractive sufficient descent property and converges globally under some mild conditions. We test the proposed algorithm by using a large set of unconstrained problems with high dimensions in CUTEr library. The numerical comparisons with the state-of-the-art algorithm CG_DESCENT illustrate that the proposed method is effective, competitive, and promising. [ABSTRACT FROM AUTHOR]

Abstract: The solution of the augmented Lagrangian related system is a key ingredient of many iterative algorithms for the solution of saddle-point problems in constrained optimization with quasi-Newton methods. However, such problems are ill-conditioned when the penalty parameter tends to zero, whereas the error vanishes as . We present a new fast method based on a splitting penalty scheme to solve such problems with a judicious prediction–correction method. We prove that, due to the adapted right-hand side, the solution of the correction step only requires the approximation of operators independent of , when is taken sufficiently small. Hence, the proposed method is as cheaper as tends to zero. We apply the two-step scheme to efficiently solve the saddle-point problem with a penalty method. Indeed, that fully justifies the interest of the vector penalty-projection methods recently proposed by Angot et al. (2008) to solve the unsteady incompressible Navier–Stokes equations, for which we give the stability result and some quasi-optimal error estimates. Moreover, the numerical experiments confirm both the theoretical analysis and the efficiency of the proposed method which produces a fast splitting solution to augmented Lagrangian or penalty problems, possibly used as a suitable preconditioner to the fully coupled system. [Copyright &y& Elsevier]

Abstract: Since the appearance of the Barzilai–Borwein (BB) step sizes strategy for unconstrained optimization problems, it received more and more attention of the researchers. It was applied in various fields of the nonlinear optimization problems and recently was also extended to optimization problems with bound constraints. In this paper, we further extend the BB step sizes to more general variational inequality (VI) problems, i.e., we adopt them in projection methods. Under the condition that the underlying mapping of the VI problem is strongly monotone and Lipschitz continuous and the modulus of strong monotonicity and the Lipschitz constant satisfy some further conditions, we establish the global convergence of the projection methods with BB step sizes. A series of numerical examples are presented, which demonstrate that the proposed methods are convergent under mild conditions, and are more efficient than some classical projection-like methods. [Copyright &y& Elsevier]

Abstract: We consider an efficient trust-region framework which employs a new nonmonotone line search technique for unconstrained optimization problems. Unlike the traditional nonmonotone trust-region method, our proposed algorithm avoids resolving the subproblem whenever a trial step is rejected. Instead, it performs a nonmonotone Armijo-type line search in direction of the rejected trial step to construct a new point. Theoretical analysis indicates that the new approach preserves the global convergence to the first-order critical points under classical assumptions. Moreover, superlinear and quadratic convergence are established under suitable conditions. Numerical experiments show the efficiency and effectiveness of the proposed approach for solving unconstrained optimization problems. [Copyright &y& Elsevier]

Abstract: A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy. [Copyright &y& Elsevier]

Abstract: This paper presents the design of walking motions of a biped robot by a computational intelligent method. The proposed method finds the parameters of the output functions that produce such motion in the closed-loop system which fulfill the requirements of stability and minimal energy control by formulating a constrained optimization problem. A set of parameters which produces periodic motions with low energy control magnitudes and its closed-loop system trajectories are shown through a numerical study case of a 3-DOF biped robot. [Copyright &y& Elsevier]

Abstract: The economic and economic statistical designs of an control chart comprise the constrained optimization problem, which involves the simultaneous use of continuous and discrete decision variables. The particle swarm optimization (PSO) technique is adapted to deal with both continuous and discrete variables as required by the optimization problem. A numerical example in the study of Rahim and Banerjee (1993) , which used the Gamma failure mechanism, is used in the current study to indicate the procedure for solving the PSO algorithm performance. The results are compared with those from Genetic Algorithm, a popular evolutionary technique in the field of control charts under the same conditions. PSO is found to be a promising method for solving the problems of inherent in the economic and economic statistical designs of an control chart. [Copyright &y& Elsevier]

Abstract: In this paper, a constraint shifting combined homotopy method for solving multi-objective programming problems with both equality and inequality constraints is presented. It does not need the starting point to be an interior point or a feasible point and hence is convenient to use. Under some assumptions, the existence and convergence of a smooth path to an efficient solution are proven. Simple numerical results are given. [Copyright &y& Elsevier]

Abstract: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [Copyright &y& Elsevier]

Abstract: In this paper, by means of an active set strategy, we present a projected spectral gradient algorithm for solving large-scale bound constrained optimization problems. A nice property of the active set estimation technique is that it can identify the active set at the optimal point without requiring strict complementary condition, which is potentially used to solve degenerated optimization problems. Under appropriate conditions, we show that this proposed method is globally convergent. We also do some numerical experiments by using some bound constrained problems from CUTEr library. The numerical comparisons with SPG, TRON, and L-BFGS-B show that the proposed method is effective and promising. [Copyright &y& Elsevier]

Abstract: In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [Copyright &y& Elsevier]

Abstract: It is well-known that the PRP conjugate gradient method with exact line search is globally and linearly convergent. If a restart strategy is used, the convergence rate of the method can be an -step superlinear/quadratic convergence. Recently, Zhang et al. [L. Zhang, W. Zhou, D.H. Li, A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence, IMA J. Numer. Anal. 26 (2006) 629–640] developed a modified PRP (MPRP) method that is globally convergent if an inexact line search is used. In this paper, we investigate the convergence rate of the MPRP method with inexact line search. We first show that the MPRP method with Armijo line search or Wolfe line search is linearly convergent. We then show that the MPRP method with a restart strategy still retains -step superlinear/quadratic convergence if the initial steplength is appropriately chosen. We also do some numerical experiments. The results show that the restart MPRP method does converge quadratically. Moreover, it is more efficient than the non-restart method. [Copyright &y& Elsevier]

Abstract: A domain decomposition method (DDM) is presented to solve the distributed optimal control problem. The optimal control problem essentially couples an elliptic partial differential equation with respect to the state variable and a variational inequality with respect to the constrained control variable. The proposed algorithm, called SA–GP algorithm, consists of two iterative stages. In the inner loops, the Schwarz alternating method (SA) is applied to solve the state and co-state variables, and in the outer loops the gradient projection algorithm (GP) is adopted to obtain the control variable. Convergence of iterations depends on both the outer and the inner loops, which are coupled and affected by each other. In the classical iteration algorithms, a given tolerance would be reached after sufficiently many iteration steps, but more iterations lead to huge computational cost. For solving constrained optimal control problems, most of the computational cost is used to solve PDEs. In this paper, a proposed iterative number independent of the tolerance is used in the inner loops so as to save a lot of computational cost. The convergence rate of -error of control variable is derived. Also the analysis on how to choose the proposed iteration number in the inner loops is given. Some numerical experiments are performed to verify the theoretical results. [Copyright &y& Elsevier]

Abstract: The paper introduces a smoothing technique for a lower order penalty function for constrained optimization problems (COP). It is proved that the optimal solution to the smoothed penalty optimization problem is a -approximate optimal solution to the original optimization problem under some mild assumptions. Based on the smoothed penalty function, an algorithm for solving COP is proposed and some numerical examples are given. [Copyright &y& Elsevier]

Abstract: We investigate a parametric method for calibrating European option pricing using the state-of-art exponential Lévy models. We propose a derivative-free calibration method constrained by four observable statistical moments (mean, variance, skewness and kurtosis) from underlying time series to conquer the ill-posed inverse problem and to incorporate priors on observable statistical moments. We present a numerical implementation scheme for calibrating the exponential Lévy models and show that it can resolve the instability of the inverse problems empirically and can produce good calibration results. In particular, we apply our approach to real market data sets of S&P 500 call options with significantly better performance. [ABSTRACT FROM AUTHOR]

Abstract: Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems. [Copyright &y& Elsevier]

Abstract: A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new spectral PRP conjugate gradient algorithm has been developed for solving unconstrained optimization problems, where the search direction was a kind of combination of the gradient and the obtained direction, and the steplength was obtained by the Wolfe-type inexact line search. It was proved that the search direction at each iteration is a descent direction of objective function. Under mild conditions, we have established the global convergence theorem of the proposed method. Numerical results showed that the algorithm is promising, particularly, compared with the existing several main methods. [ABSTRACT FROM AUTHOR]

Abstract: A numerical algorithm is presented to solve the constrained weighted energy problem from potential theory. As one of the possible applications of this algorithm, we study the convergence properties of the rational Lanczos iteration method for the symmetric eigenvalue problem. The constrained weighted energy problem characterizes the region containing those eigenvalues that are well approximated by the Ritz values. The region depends on the distribution of the eigenvalues, on the distribution of the poles, and on the ratio between the size of the matrix and the number of iterations. Our algorithm gives the possibility of finding the boundary of this region in an effective way. We give numerical examples for different distributions of poles and eigenvalues and compare the results of our algorithm with the convergence behavior of the explicitly performed rational Lanczos algorithm. [ABSTRACT FROM AUTHOR]

Abstract: New accelerated nonlinear conjugate gradient algorithms which are mainly modifications of Dai and Yuan’s for unconstrained optimization are proposed. Using the exact line search, the algorithm reduces to the Dai and Yuan conjugate gradient computational scheme. For inexact line search the algorithm satisfies the sufficient descent condition. Since the step lengths in conjugate gradient algorithms may differ from 1 by two orders of magnitude and tend to vary in a very unpredictable manner, the algorithms are equipped with an acceleration scheme able to improve the efficiency of the algorithms. Computational results for a set consisting of 750 unconstrained optimization test problems show that these new conjugate gradient algorithms substantially outperform the Dai–Yuan conjugate gradient algorithm and its hybrid variants, Hestenes–Stiefel, Polak–Ribière–Polyak, CONMIN conjugate gradient algorithms, limited quasi-Newton algorithm LBFGS and compare favorably with CG_DESCENT. In the frame of this numerical study the accelerated scaled memoryless BFGS preconditioned conjugate gradient ASCALCG algorithm proved to be more robust. [Copyright &y& Elsevier]

Abstract: In this paper, an iterative method is presented for the computation of regularized solutions of discrete ill-posed problems. In the proposed method, the regularization problem is formulated as an equality constrained minimization problem and an iterative Lagrange method is used for its solution. The Lagrange iteration is terminated according to the discrepancy principle. The relationship between the proposed approach and classical Tikhonov regularization is discussed. Results of numerical experiments are presented to illustrate the effectiveness and usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Optimization of directional over-current relay (DOCR) settings is an important problem in electrical engineering. The optimization model of the problem turns out to be non-linear and highly constrained in which two settings namely time dial setting (TDS) and plug setting (PS) of each relay are considered as decision variables; the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones, is considered as an objective function. In the present study, three models are considered namely IEEE 3-bus model, IEEE 4-bus model and IEEE 6-bus model. To solve the problem, we have applied five newly developed versions of differential evolution (DE) called modified DE versions (MDE1, MDE2, MDE3, MDE4, and MDE5). The results are compared with the classical DE algorithm and with five more algorithms available in the literature; the numerical results show that the modified DE algorithms outperforms or perform at par with the other algorithms. [Copyright &y& Elsevier]

Abstract: Aircraft sizing studies consist in determining the main characteristics of an aircraft starting from a set of requirements. These studies can be summarized as global constrained optimization problems. The constraints express physical feasibility and the requirements to be satisfied; the objectives are market-driven performances of the aircraft. These optimizations are currently manually conducted as many input data frequently evolve during the study. This work introduced mathematical methods that are useful in a sizing tool to ease, fasten and enhance the aircraft configuration optimization problem. Using genetic algorithms, large amounts of design points satisfying the requirements were rapidly produced, despite some issues inherent to the aircraft model: numerical noise or physically meaningless design points due to the vast design space. Then, multicriteria optimization methods were introduced, as several criteria were considered concurrently. As calculation times became important, the aircraft model was substituted by a surrogate model. Radial basis functions approximated the constraint and the objective functions. Finally, a possible outcome of the integration of these different techniques was proposed in order to yield the engineers a global and operational perception of the design space. [Copyright &y& Elsevier]

Abstract: In this paper, a new feasible primal–dual interior point algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The searching direction is feasible and the object function is monotone decreasing. The proposed algorithm is proved to possess global and superlinear convergence under mild conditions. Finally, some numerical experiments with the algorithm are reported. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The main application is dynamic contact problems. The principle consists in the use of a singular mass matrix obtained by the mean of different discretizations of the solution and of its time derivative. We prove that the semi-discretized problem is well-posed and energy conserving. Numerical experiments show that this is a crucial property to build stable numerical schemes. [Copyright &y& Elsevier]

Abstract: Recently there have two different effective methods proposed by Kanzow et al. in (Kanzow, 2001 ) and (Kanzow and Petra, 2004 ), respectively, which commonly use the Fischer–Burmeister (FB) function to recast the mixed complementarity problem (MCP) as a constrained minimization problem and a nonlinear system of equations, respectively. They all remark that their algorithms may be improved if the FB function is replaced by other NCP functions. Accordingly, in this paper, we employ the generalized Fischer–Burmeister (GFB) where the 2-norm in the FB function is relaxed to a general -norm () for the two methods and investigate how much the improvement is by changing the parameter as well as which method is influenced more when we do so, by the performance profiles of iterations and function evaluations for the two methods with different on MCPLIB collection. [Copyright &y& Elsevier]

Abstract: In this paper, we propose some improvements on a new gradient-type method for solving large-scale unconstrained optimization problems, in which we use data from two previous steps to revise the current approximate Hessian. The new method which we considered, resembles to that of Barzilai and Borwein (BB) method. The innovation features of this approach consist in using approximation of the Hessian in diagonal matrix form based on the modified weak secant equation rather than the multiple of the identity matrix in the BB method. Using this approach, we can obtain a higher order accuracy of Hessian approximation when compares to other existing BB-type method. By incorporating a simple monotone strategy, the global convergence of the new method is achieved. Practical insights into the effectiveness of the proposed method are given by numerical comparison with the BB method and its variant. [Copyright &y& Elsevier]

Abstract: In this paper, a simple feasible SQP method for nonlinear inequality constrained optimization is presented. At each iteration, we need to solve one QP subproblem only. After solving a system of linear equations, a new feasible descent direction is designed. The Maratos effect is avoided by using a high-order corrected direction. Under some suitable conditions the global and superlinear convergence can be induced. In the end, numerical experiments show that the method in this paper is effective. [Copyright &y& Elsevier]

Abstract: The balanced Procrustes problem with some special constraints such as symmetric orthogonality and symmetric idempotence are considered. By one time eigenvalue decomposition of the matrix product generated by the matrices and , the constrained solutions are constructed simply. Similar strategy is applied to the problem with the corresponding -commuting constraints with a given symmetric matrix . Numerical examples are presented to show the efficiency of the proposed methods. [Copyright &y& Elsevier]

Abstract: Solving a variational inequality problem can be equivalently reformulated into solving a unconstraint optimization problem where the corresponding objective function is called a merit function. An important class of merit function is the generalized D-gap function introduced in [N. Yamashita, K. Taji, M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, J. Optim. Theory Appl. 92 (1997) 439–456] and Yamashita and Fukushima (1997) . In this paper, we present new fractional local/global error bound results for the generalized D-gap functions of nonsmooth variational inequality problems, which gives an effective estimate on the distance between a specific point to the solution set, in terms of the corresponding function value of the generalized D-gap function. Numerical examples and a simple application to the free boundary problem are also presented to illustrate the significance of our error bound results. [Copyright &y& Elsevier]

Abstract: Recently, a continuous method has been proposed by Golub and Liao as an alternative way to solve the minimum and interior eigenvalue problems. According to their numerical results, their method seems promising. This article is an extension along this line. In this article, firstly, we convert an eigenvalue problem to an equivalent constrained optimization problem. Secondly, using the Karush–Kuhn–Tucker conditions of this equivalent optimization problem, we obtain a variant of the Rayleigh quotient gradient flow, which is formulated by a system of differential-algebraic equations. Thirdly, based on the Rayleigh quotient gradient flow, we give a practical numerical method for the minimum and interior eigenvalue problems. Finally, we also give some numerical experiments of our method, the Golub and Liao method, and EIGS (a Matlab implementation for computing eigenvalues using restarted Arnoldi’s method) for some typical eigenvalue problems. Our numerical experiments indicate that our method seems promising for most test problems. [Copyright &y& Elsevier]

Abstract: A derivative-free simulated annealing driven multi-start algorithm for continuous global optimization is presented. We first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient-based trial point generation. We then suitably embed the multi-start procedure within the simulated annealing algorithm. We modify the derivative-free pattern search method and use it as the local search in the multi-start procedure. We study the convergence properties of the algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with a gradient-based simulated annealing algorithm and three population-based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms, specially for problems requiring ‘direct search’ type algorithm. [Copyright &y& Elsevier]

Abstract: We propose a novel hybrid algorithm named PSO-DE, which integrates particle swarm optimization (PSO) with differential evolution (DE) to solve constrained numerical and engineering optimization problems. Traditional PSO is easy to fall into stagnation when no particle discovers a position that is better than its previous best position for several generations. DE is incorporated into update the previous best positions of particles to force PSO jump out of stagnation, because of its strong searching ability. The hybrid algorithm speeds up the convergence and improves the algorithm’s performance. We test the presented method on 11 well-known benchmark test functions and five engineering optimization functions. Comparisons show that PSO-DE outperforms or performs similarly to seven state-of-the-art approaches in terms of the quality of the resulting solutions. [Copyright &y& Elsevier]

Abstract: In this work, we reformulate the inverse optimal value problem equivalently as a corresponding nonlinear bilevel programming (BLP) problem. For the nonlinear BLP problem, the duality gap of the lower level problem is appended to the upper level objective with a penalty, and then a penalized problem is obtained. On the basis of the concept of partial calmness, we prove that the penalty function is exact. Then, an algorithm is proposed and an inverse optimal value problem is resolved to illustrate the algorithm. [Copyright &y& Elsevier]