Month: September 2015

Regularized HPE-type methods for solving monotone inclusions with improved pointwise iteration-complexity bounds

  • M. Marques Alves
  • Renato D.C. Monteiro
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the standard HPE method applied to regularizations of the original MIP. It is shown that its pointwise iteration-complexity considerably improves the one of the HPE method … Read more

    A basis-free null space method for solving generalized saddle point problems

  • Maria A. Diniz-Ehrhardt
  • Lucas G. Pedroso
  • Douglas Mendes
    • Categories Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , , ,

    Using an augmented Lagrangian matrix approach, we analytically solve in this paper a broad class of linear systems that includes symmetric and nonsymmetric problems in saddle point form. To this end, some mild assumptions are made and a preconditioning is specially designed to improve the sensitivity of the systems before the calculation of their solutions. … Read more

    Strong Duality: Without Simplex and without theorems of alternatives

  • Somdeb Lahiri
    • Categories Linear Programming Tags , ,

    The simplex method has its own problems related to degenerate basic feasible solutions. While such solutions are infrequent, from a theoretical standpoint a proof of the strong duality theorem that uses the simplex method is not complete until it has taken a few extra steps. Further, for economists the duality theorem is extremely important whereas … Read more

    A Practical Scheme to Compute Pessimistic Bilevel Optimization Problem

  • Bo Zeng
    • Categories Complementarity and Variational Inequalities, Game Theory Tags ,

    In this paper, we present a new computation scheme for pessimistic bilevel optimization problem, which so far does not have any computational methods generally applicable yet. We first develop a tight relaxation and then design a simple scheme to ensure a feasible and optimal solution. Then, we discuss using this scheme to compute linear pessimistic … Read more

    Local monotonicity and full stability for parametric variational systems

  • Boris S. Mordukhovich
  • Tran Nghia
    • Categories Nonsmooth Optimization Tags , ,

    The paper introduces and characterizes new notions of Lipschitzian and H\”olderian full stability of solutions to general parametric variational systems described via partial subdifferential of prox-regular functions acting in finite-dimensional and Hilbert spaces. These notions, postulated certain quantitative properties of single-valued localizations of solution maps, are closely related to local strong maximal monotonicity of associated … Read more

    A Stochastic Programming Approach for Shelter Location and Evacuation Planning

  • Vedat Bayram
  • Hande Yaman
    • Categories Second-Order Cone Programming, Stochastic Programming, Transportation Tags , , , , ,

    Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers … Read more

    A new explicit iterative algorithm for solving split variational inclusion and fixed point problem for the infinite family of nonexpansive operators

  • Zhihui Xu
  • Cuijie Zhang
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new explicit iterative algorithm for finding a solution of split variational inclusion problem over the common fixed points set of a infinite family of nonexpansive mappings in Hilbert spaces. To reach this goal, the iterative algorithms which combine Tian’s method with some fixed point technically proving methods are utilized … Read more

    Newton-like method with diagonal correction for distributed optimization

  • Dragana Bajović
  • Dušan Jakovetić
  • Nataša Krejić
  • Nataša Krklec Jerinkić
    • Categories Nonlinear Optimization Tags , , ,

    We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second-order information … Read more

    Variational principles, completeness and the existence of traps in behavioral sciences

  • Stephan Cobzas
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - Science and Engineering, Nonlinear Optimization

    In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland’s variational principle in such spaces, and provide examples illustrating significant improvements to some previously obtained results, even in complete metric spaces. At the behavioral level, we show that the … Read more

    Remark on multi-target,robust linear-quadratic control problem on semi-infinite interval

  • Leonid Faybusovich
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization Tags ,

    We consider multi-target,robust linear-quadratic control problem on semi-infinite interval. Using functional-analytic approach developed in [2], we reduce this problem to a convex optimization problem on the simplex. Explicit procedure for the reduced optimization problem is described. CitationPreprint, University of Notre Dame, August,2015ArticleDownload View PDF