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Abstract: This paper presents an optimization technique for solving a maximum flow problem arising in widespread applications in a variety of settings. On the basis of the Karush–Kuhn–Tucker (KKT) optimality conditions, a neural network model is constructed. The equilibrium point of the proposed neural network is then proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the maximum flow problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper. [Copyright &y& Elsevier]

In this paper, we consider damping optimization in mechanical system excited by an external force. We use optimization criteria based on minimizing average energy amplitude and average displacement amplitude over the arbitrary time. As the main result we derive explicit formulas for objective functions. These formulas can be implemented efficiently and accelerate optimization process significantly, which is illustrated in a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, new classes of nondifferentiable functions constituting multiobjective programming problems are introduced. Namely, the classes of --type I objective and constraint functions and, moreover, the various classes of generalized --type I objective and constraint functions are defined for directionally differentiable multiobjective programming problems. Sufficient optimality conditions and various Mond–Weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type. Finally, it is showed that the introduced --type I notion with is not a sufficient condition for Wolfe weak duality to hold. These results are illustrated in the paper by suitable examples. [Copyright &y& Elsevier]

In this paper, we study planar quintic G 2 Hermite interpolation with minimum strain energy. To match arbitrary G 2 Hermite data, a quintic curve is expressed in terms of four free parameters that encode the local reparameterization at the endpoints and are available for further optimization. We express the approximate strain energy as a quartic function in four parameters, whose minimum can be found by solving an optimization problem of two parameters relating to the magnitudes of endpoint tangent vectors. A feasible region is used while searching the optimal values of these two parameters such that the interpolating curve can preserve tangent directions and avoid singularities at the endpoints. We then solve this constrained minimization problem via the proximal gradient method. Several comparative examples are provided to demonstrate the effectiveness of the proposed method and applications to shape design are also shown. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a new barrier function for primal–dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal–dual interior-point methods. [Copyright &y& Elsevier]

Abstract: In this paper, we study global concave optimization by the canonical dual function. A differential flow on the dual feasible space is introduced. We show that the flow reaches a global minimizer of the concave function over a box. An example is illustrated. [ABSTRACT FROM AUTHOR]

Abstract: Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques. [Copyright &y& Elsevier]

Abstract: This paper analyzes the -policy M/M/1/K queueing system with working vacation and an exponential startup time. The -policy deals with the issue of controlling arrivals to a queueing system, and the server requires a startup time before allowing customers to enter the system. For the queueing systems with working vacation, the server can still provide service to customers rather than completely stop the service during a vacation period. The matrix-analytic method is applied to develop the steady-state probabilities, and then obtain several system characteristics. We construct the expected cost function and formulate an optimization problem to find the minimum cost. The direct search method and Quasi-Newton method are implemented to determine the optimal system capacity , the optimal threshold and the optimal service rates at the minimum cost. A sensitivity analysis is conducted to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical examples are provided for illustration purpose. [Copyright &y& Elsevier]

Abstract: In this paper, the canonical dual function (Gao, 2004 ) is used to solve a global optimization. We find global minimizers by backward differential flows. The backward flow is created by the local solution to the initial value problem of an ordinary differential equation. Some examples and applications are presented. [Copyright &y& Elsevier]

Abstract: Functions with poles occur in many branches of applied mathematics which involve resonance phenomena. Such functions are challenging to interpolate, in particular in higher dimensions. In this paper we develop a technique for interpolation with quotients of two radial basis function (RBF) expansions to approximate such functions as an alternative to rational approximation. Since the quotient is not uniquely determined we introduce an additional constraint, the sum of the RBF-norms of the numerator and denominator squared should be minimal subjected to a norm condition on the function values. The method was designed for antenna design applications and we show by examples that the scattering matrix for a patch antenna as a function of some design parameters can be approximated accurately with the new method. In many cases, e.g. in antenna optimization, the function evaluations are time consuming, and therefore it is important to reduce the number of evaluations but still obtain a good approximation. A sensitivity analysis of the new interpolation technique is carried out and it gives indications how efficient adaptation methods could be devised. A family of such methods are evaluated on antenna data and the results show that much performance can be gained by choosing the right method. [Copyright &y& Elsevier]

Abstract: This paper presents a mathematical model of trade-off relations arising in third party logistics using Pareto optimal solutions for multi-objective optimization problems. The model defines an optimal set of distribution costs and service levels constituting a trade-off relation. An analogy to the concept of the indifference curve in the field of economics is discussed. Numerical experiments for a simplified problem are performed, demonstrating an increasing process of the utility of logistics. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem. [Copyright &y& Elsevier]

Abstract: This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables–aerofoil sections–supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality. [Copyright &y& Elsevier]

Abstract: This paper is the first to discuss the communal home meal delivery problem. The problem can be modelled as a multiple travelling salesman problem with time windows, that is closely related to the well-studied vehicle routing problem with time windows. Experimental results are reported for a real-life case study from Central Finland over several alternative scenarios using the SPIDER commercial solver. The comparison with current practice reveals that a significant savings potential can be obtained using off-the-shelf optimization tools. As such, the potential for supporting real-life communal routing problems can be considered to be important for VRP practitioners. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a modified BFGS (Broyden–Fletcher–Goldfarb–Shanno) method with nonmonotone line search for unconstrained optimization. Under some mild conditions, we show that the method is globally convergent without a convexity assumption on the objective function. We also report some preliminary numerical results to show the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: The parameterized Uzawa preconditioners for saddle point problems are studied in this paper. The eigenvalues of the preconditioned matrix are located in (0, 2) by choosing the suitable parameters. Furthermore, we give two strategies to optimize the rate of convergence by finding the suitable values of parameters. Numerical computations show that the parameterized Uzawa preconditioners can lead to practical and effective preconditioned GMRES methods for solving the saddle point problems. [Copyright &y& Elsevier]

Abstract: In this paper, by means of a new efficient identification technique of active constraints and the method of strongly sub-feasible direction, we propose a new sequential system of linear equations (SSLE) algorithm for solving inequality constrained optimization problems, in which the initial point is arbitrary. At each iteration, we first yield the working set by a pivoting operation and a generalized projection; then, three or four reduced linear equations with a same coefficient are solved to obtain the search direction. After a finite number of iterations, the algorithm can produced a feasible iteration point, and it becomes the method of feasible directions. Moreover, after finitely many iterations, the working set becomes independent of the iterates and is essentially the same as the active set of the KKT point. Under some mild conditions, the proposed algorithm is proved to be globally, strongly and superlinearly convergent. Finally, some preliminary numerical experiments are reported to show that the algorithm is practicable and effective. [Copyright &y& Elsevier]

Abstract: Although the Liu–Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak–Ribière–Polyak (PRP) and Hestenes–Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo–Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported. [Copyright &y& Elsevier]

Abstract: In this paper, a new filled function which has better properties is proposed for identifying a global minimum point for a general class of nonlinear programming problems within a closed bounded domain. An algorithm for unconstrained global optimization is developed from the new filled function. Theoretical and numerical properties of the proposed filled function are investigated. The implementation of the algorithm on seven test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: In this paper, we present a nonmonotone conic trust region method based on line search technique for unconstrained optimization. The new algorithm can be regarded as a combination of nonmonotone technique, line search technique and conic trust region method. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength satisfies some line search condition. The function value can only be allowed to increase when trial steps are not accepted in close succession of iterations. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the existing methods. [Copyright &y& Elsevier]

Abstract: This paper deals with two different optimization techniques to solve the bound-constrained nonlinear optimization problems based on division criteria of a prescribed search region, finite interval arithmetic and interval ranking in the context of a decision maker’s point of view. In the proposed techniques, two different division criteria are introduced where the accepted region is divided into several distinct subregions and in each subregion, the objective function is computed in the form of an interval using interval arithmetic and the subregion containing the best objective value is found by interval ranking. The process is continued until the interval width for each variable in the accepted subregion is negligible. In this way, the global optimal or close to global optimal values of decision variables and the objective function can easily be obtained in the form of an interval with negligible widths. Both the techniques are applied on several benchmark functions and are compared with the existing analytical and heuristic methods. [Copyright &y& Elsevier]

Abstract: In this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems. A new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions. In particular, Polak–Ribiére–Polyak and Liu–Storey conjugate gradient methods are special cases of the new class of conjugate gradient methods. By estimating the local Lipschitz constant of the derivative of objective functions, we can find an adequate step size and substantially decrease the function evaluations at each iteration. Numerical results show that these new conjugate gradient methods are effective in minimizing large-scale non-convex non-quadratic functions. [Copyright &y& Elsevier]

Abstract: Multiplicative programming problems with exponent (MPE) have many practical applications in various fields. In this paper, a method for accelerating global optimization is proposed for a class of multiplicative programming problems with exponent under multiplicative constraints using a suitable deleting technique. This technique offers the possibility of cutting away a large part of the currently investigated region in which the globally optimal solution of the MPE does not exist. The deleting technique can accelerate the convergence of the proposed global optimization algorithm. Two numerical examples are given to illustrate the feasibility of the deleting technique. [Copyright &y& Elsevier]

Abstract: In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a nonmonotone technique for solving unconstrained optimization. The local and global convergence properties are proved under reasonable assumptions. Numerical experiments are conducted to compare this method with the method of [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231]. [Copyright &y& Elsevier]

Abstract: Bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure. They are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem. In this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative, the lower level one is linear and the common constraint region is a bounded polyhedron. After replacing the lower level problem by its Karush–Kuhn–Tucker conditions, the existence of an extreme point which solves the problem is proved by using a penalty function approach. Besides, an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution. Finally, we generalise the problem by including upper level constraints which involve both level variables. [Copyright &y& Elsevier]

Abstract: This paper deals with the stability of linear semi-infinite programming (LSIP, for short) problems. We characterize those LSIP problems from which we can obtain, under small perturbations in the data, different types of problems, namely, inconsistent, consistent unsolvable, and solvable problems. The problems of this class are highly unstable and, for this reason, we say that they are totally ill-posed. The characterization that we provide here is of geometrical nature, and it depends exclusively on the original data (i.e., on the coefficients of the nominal LSIP problem). Our results cover the case of linear programming problems, and they are mainly obtained via a new formula for the subdifferential mapping of the support function. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a higher-order Mond–Weir dual for a set-valued optimization problem by virtue of higher-order contingent derivatives and discuss their weak duality, strong duality and converse duality properties. [Copyright &y& Elsevier]

Abstract: Efficiency could be not only the ratio of weighted sum of outputs to that of inputs but also that of weighted sum of inputs to that of outputs. When the previous efficiency measures the best relative efficiency within the range of no more than one, the decision-making units (DMUs) who get the optimum value of one perform best among all the DMUs. If the previous efficiency is measured within the range of no less than one, the DMUs who get the optimum value of one perform worst among all the DMUs. When the later efficiency is measured within the range of no more than one, the DMUs who get the optimum value of one perform worst among all the DMUs. If the later efficiency is measured within the range of no less than one, the DMUs who get the optimum value of one perform best among all the DMUs. This paper mainly studies an interval DEA model with later efficiency, in which efficiency is measured within the range of an interval, whose upper bound is set to one and the lower bound is determined by introducing a virtual ideal DMU, whose performance is definitely superior to any DMUs. The efficiencies, obtained from interval DEA model, turn out to be all intervals and are referred to as interval efficiencies, which combine the best and the worst relative efficiency in a reasonable manner to give an overall assessment of performances for all DMUs. Assessor''s preference information on input and output weights is also incorporated into interval DEA model reasonably and conveniently. Through an example, some differences are found from the ranking results obtained from interval DEA model and bounded DEA model using the Hurwicz criterion approach to rank the interval efficiencies. [Copyright &y& Elsevier]

Abstract: This paper analyzes a certain type of impulsive differential equations (IDEs). Several useful theorems for its periodic solutions and their stabilities are given. The key idea is that a periodically time-dependent IDE can be transformed into the state-dependent IDE. As applications of our theory, the optimization problems in population dynamics are studied. That is, the maximum sustainable yields of single population models with periodically impulsive constant harvesting are discussed. Furthermore, we apply these results to the studies of the order-1 periodic solutions and their stability of a single population model with stage structure in which the mature is impulsively proportionally harvested while the immature is impulsively added with the constant. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new trust region method for unconstrained optimization problems. The new trust region method can automatically adjust the trust region radius of related subproblems at each iteration and has strong global convergence under some mild conditions. We also analyze the global linear convergence, local superlinear and quadratic convergence rate of the new method. Numerical results show that the new trust region method is available and efficient in practical computation. [Copyright &y& Elsevier]

Abstract: In this paper we propose a nonmonotone trust region method. Unlike traditional nonmonotone trust region method, the nonmonotone technique applied to our method is based on the nonmonotone line search technique proposed by Zhang and Hager [A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14(4) (2004) 1043–1056] instead of that presented by Grippo et al. [A nonmonotone line search technique for Newton''s method, SIAM J. Numer. Anal. 23(4) (1986) 707–716]. So the method requires nonincreasing of a special weighted average of the successive function values. Global and superlinear convergence of the method are proved under suitable conditions. Preliminary numerical results show that the method is efficient for unconstrained optimization problems. [Copyright &y& Elsevier]

Abstract: In this paper the authors present a necessary condition for minimum of a functional in the case in which the function L is continuous but not of class . This situation arises in problems of optimization of hydrothermal systems with pumped-storage plants. In such problems, the function is discontinuous in , which is the borderline point between the power generation zone and the pumping zone . The problem can be naturally formulated in the framework of nonsmooth analysis, using the generalized (or Clarke''s) gradient. [Copyright &y& Elsevier]

In this paper, we modify the trust region interior point algorithm proposed by Bonnans and Pola in (SIAM J. Optim. 7(3) (1997) 717) for linear constrained optimization. A mixed strategy using both trust region and line-search techniques is adopted which switches to back-tracking steps when a trial step produced by the trust region subproblem may be unacceptable. The global convergence and local convergence rate of the improved algorithm are established under some reasonable conditions. A nonmonotonic criterion is used to speed up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]