Other Topics

Smoothness Properties of a Regularized Gap Function for Quasi-Variational Inequalities

  • Nadja Harms
  • Oliver Stein
  • Christian Kanzow
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Game Theory Tags , , , , ,

    This article studies continuity and differentiability properties for a reformulation of a finite-dimensional quasi-variational inequality (QVI) problem using a regularized gap function approach. For a special class of QVIs, this gap function is continuously differentiable everywhere, in general, however, it has nondifferentiability points. We therefore take a closer look at these nondifferentiability points and show, … Read more

    Optimal Power Grid Protection through A Defender-Attacker-Defender Model

  • Wei Yuan
  • Bo Zeng
  • Long Zhao
    • Categories Applications - Science and Engineering, Game Theory

    Power grid vulnerability is a major concern of modern society, and its protection problem is often formulated as a tri-level defender-attacker-defender model. However, this tri-level problem is compu- tationally challenging. In this paper, we design and implement a Column-and-Constraint Generation algorithm to derive its optimal solutions. Numerical results on an IEEE system show that: (i) … Read more

    Principle of optimal accuracy classification for metrological purposes

  • David Kisets
    • Categories Applications - Science and Engineering, Other Topics

    The conceptions of optimizing a quantitative classification hierarchy and the criterion of informational optimality have been used for modeling universal accuracy classification scale. Proposed model is based on test uncertainty ratios determined in conformity with optimal levels of confidence in evaluating measurement uncertainty, as well as on the optimal classification structure. The author believes that … Read more

    Lot Sizing with Piecewise Concave Production Costs

  • M. Selim Akturk
  • Esra Koca
  • Hande Yaman
    • Categories Dynamic Programming

    We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming (DP) algorithm to solve this problem and answer an open question in the … Read more

    A New Error Bound Result for Generalized Nash Equilibrium Problems and its Algorithmic Application

  • Axel Dreves
  • Francisco Facchinei
  • Andreas Fischer
  • Markus Herrich
    • Categories Complementarity and Variational Inequalities, Game Theory, Nonlinear Optimization Tags , , , , ,

    We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local convergence theory on an error bound and provide a new sufficient condition for it to hold that … Read more

    Equivalence of an Approximate Linear Programming Bound with the Held-Karp Bound for the Traveling Salesman Problem

  • Alejandro Toriello
    • Categories Combinatorial Optimization, Dynamic Programming, Integer Programming Tags , , ,

    We consider two linear relaxations of the asymmetric traveling salesman problem (TSP), the Held-Karp relaxation of the TSP’s arc-based formulation, and a particular approximate linear programming (ALP) relaxation obtained by restricting the dual of the TSP’s shortest path formulation. We show that the two formulations produce equal lower bounds for the TSP’s optimal cost regardless … 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

    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. Citation Published in Constructive Nonsmooth Analysis and Related Topics (Vladimir Demyanov, Panos M. … Read more

    STOCHASTIC OPTIMIZATION OVER A PARETO SET ASSOCIATED WITH A STOCHASTIC MULTI-OBJECTIVE OPTIMIZATION PROBLEM

  • Henri Bonnel
  • Julien Collonge
    • Categories Multi-Criteria Optimization, Stochastic Approaches Tags , , , ,

    We deal with the problem of minimizing the expectation of a real valued random function over the weakly Pareto or Pareto set associated with a Stochastic Multi-Objective Optimization Problem (SMOP) whose objectives are expectations of random functions. Assuming that the closed form of these expectations is difficult to obtain, we apply the Sample Average Approximation … Read more

    Risk-Averse Control of Undiscounted Transient Markov Models

  • Özlem Cavus
  • Andrzej Ruszczyński
    • Categories Dynamic Programming, Stochastic Programming

    We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping … Read more