Variable Metric Forward-Backward algorithm for minimizing the sum of a differentiable function and a convex function

  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Audrey Repetti
    • Categories Nonsmooth Optimization

    We consider the minimization of a function $G$ defined on $R^N$, which is the sum of a (non necessarily convex) differentiable function and a (non necessarily differentiable) convex function. Moreover, we assume that $G$ satisfies the Kurdyka-Lojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm may suffer from … Read more

    AN EFFICIENT ALGORITHM FOR SECOND-ORDER CONE LINEAR COMPLEMENTARITY PROBLEMS

  • Weihong Yang
  • Lei-Hong Zhang
    • Categories Complementarity and Variational Inequalities, Second-Order Cone Programming Tags , , , ,

    Recently, the globally uniquely solvable (GUS) property of the linear transformation $M\in R^{n\times n}$ in the second-order cone linear complementarity problem (SOCLCP) receives much attention and has been studied substantially. Yang and Yuan [30] contributed a new characterization of the GUS property of the linear transformation, which is formulated by basic linear-algebra-related properties. In this … Read more

    Public Facility Location Using Dispersion, Population, and Equity Criteria

  • Rajan Batta
  • Miguel A. Lejeune
  • Srinivas Prasad
    • Categories Facility Planning and Design, Production and Logistics Tags , ,

    Administrators/Decision Makers (DMs) responsible for making locational decisions for public facilities have many other overriding factors to consider that dominate traditional OR/MS objectives that relate to response time. We propose that an appropriate role for the OR/MS analyst is to help the DMs identify a good set of solutions rather than an optimal solution that … Read more

    Effectiveness-Equity Models for Facility Location Problems on Tree Networks

  • Miguel A. Lejeune
  • Srinivas Prasad
    • Categories Convex Optimization, Multi-Criteria Optimization, Production and Logistics

    We propose models to investigate effectiveness-equity tradeoffs in tree network facility location problems. We use the commonly used median objective as a measure of effectiveness, and the Gini index as a measure of (in)equity, and formulate bicriteria problems involving these objectives. We develop procedures to identify an efficient set of solutions to these problems, analyze … Read more

    An Extragradient-Based Alternating Direction Method for Convex Minimization

  • Tianyi Lin
  • Shiqian Ma
  • Shuzhong Zhang
    • Categories Convex and Nonsmooth Optimization

    In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one … Read more

    Multidirectional Physarum Solver: an Innovative Bio-inspired Algorithm for Optimal Discrete Decision Making

  • Luca Masi
  • Massimiliano Vasile
    • Categories Combinatorial Optimization Tags , , , , ,

    This paper introduces a new bio-inspired algorithm for optimal discrete decision making, able to incrementally grow and explore decision graphs in multiple directions. The heuristic draws inspiration from the idea that building decision sequences from multiple directions and then combining the sequences is an optimal choice if compared with a unidirectional approach. The behaviour of … Read more

    Well-posedness for Lexicographic Vector Equilibrium Problems

  • L. Q. Anh
  • Alexander Y. Kruger
  • T. Q. Duy
  • Nguyen H. Thao
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization Tags , ,

    We consider lexicographic vector equilibrium problems in metric spaces. Sufficient conditions for a family of such problems to be (uniquely) well-posed at the reference point are established. As an application, we derive several results on well-posedness for a class of variational inequalities. CitationPublished in Constructive Nonsmooth Analysis and Related Topics (Vladimir Demyanov, Panos M. Pardalos, … Read more

    Biased and unbiased random-key genetic algorithms: An experimental analysis

  • José Fernando Gonçalves
  • Mauricio G.C. Resende
  • Rodrigo F. Toso
    • Categories Meta Heuristics, Optimization Software Benchmark, Stochastic Approaches Tags , , , , , ,

    We study the runtime performance of three types of random-key genetic algorithms: the unbiased algorithm of Bean (1994); the biased algorithm of Gonçalves and Resende (2011); and a greedy version of Bean’s algorithm on 12 instances from four types of covering problems: general-cost set covering, Steiner triple covering, general-cost set K-covering, and unit-cost covering by … Read more

    Calmness modulus of linear semi-infinite programs

  • M.J. Cánovas
  • Alexander Y. Kruger
  • Marco A. López
  • J. Parra
  • Michel Thera
    • Categories Linear Programming, Semi-infinite Programming Tags , , , ,

    Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide … Read more

    On the Augmented Lagrangian Dual for Integer Programming

  • Natashia Boland
  • Andrew C. Eberhard
    • Categories (Mixed) Integer Linear Programming Tags , ,

    We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a … Read more