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A gradient-based approach for computing Nash equilibria of large sequential games

  • Andrew Gilpin
  • Javier F. Peña
  • Samid Hoda
    • Categories Convex Optimization, Game Theory, Linear Programming Tags , ,

    We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem. Citation Working Paper, Tepper School of Business, Carnegie Mellon University Article Download View A gradient-based approach for computing … Read more

    Optimization for Simulation: LAD Accelerator

  • Miguel A. Lejeune
  • François Margot
    • Categories Data-Mining, Optimization of Simulated Systems, Stochastic Approaches Tags , ,

    The goal of this paper is to address the problem of evaluating the performance of a system running under unknown values for its stochastic parameters. A new approach called LAD for Simulation, based on simulation and classification software, is presented. It uses a number of simulations with very few replications and records the mean value … Read more

    On the solution of stochastic multiobjective integer linear programming problems with a parametric study

  • Osama E. Imam
  • Omar M. Saad
    • Categories Integer Programming, Multi-Criteria Optimization, Stochastic Programming

    In this study we consider a multiobjective integer linear stochastic programming problem with individual chance constraints. We assume that there is randomness in the right-hand sides of the constraints only and that the random variables are normally distributed. Some stability notions for such problem are characterized. An auxiliary problem is discussed and an algorithm as … Read more

    Objective space for multiple objectives linear fractional programming

  • Ragabia Sallam
  • Said Tantawy
    • Categories Multi-Criteria Optimization Tags , , , ,

    In this paper we give the construction of the objective space of multiple objectives linear fractional programming (MOLFP) with equal denominators under the linear fractional mapping .In this case the decision space maps to an objective space of less dimension. The important of this study is that the decision-Maker may depend on extreme points of … Read more

    A new method for solving linear fractional programming problems

  • Said Tantawy
    • Categories Other Topics

    In this paper a new method is suggested for solving the problem in which the objective function is a linear fractional function, and where the constraint functions are in the form of linear inequalities. The proposed method is based mainly upon solving this problem algebraically using the concept of duality. Since the earlier methods based … Read more

    A novel elitist multiobjective optimization algorithm: multiobjective extremal optimization

  • Min-Rong Chen
  • Yong-Zai Lu
    • Categories Approximation Algorithms, Meta Heuristics, Multi-Criteria Optimization

    Recently, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in multiobjective optimization and proposes a new novel elitist multiobjective algorithm, called Multiobjective Extremal Optimization (MOEO). In order to extend EO to solve the multiobjective … Read more

    Sufficient Conditions for a Real Polynomial to be a Sum of Squares

  • Jean-Bernard Lasserre
    • Categories Global Optimization Theory, Linear Programming, Other Topics

    We provide explicit sufficient conditions for a polynomial $f$ to be a sum of squares (s.o.s.), linear in the coefficients of $f$. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most $2d$. We also provide a simple condition to ensure … Read more

    Multi-objective branch-and-bound. Application to the bi-objective spanning tree problem.

  • Francis Sourd
  • Olivier Spanjaard
    • Categories Multi-Criteria Optimization

    This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that … Read more

    Measures with zeros in the inverse of their moment matrix

  • J. William Helton
  • Jean-Bernard Lasserre
  • M. Putinar
    • Categories Other Topics, Statistics

    We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this … Read more

    The Impact of Collusion on the Price of Anarchy in Nonatomic and Discrete Network Games

  • Tobias Harks
    • Categories Game Theory, Network Optimization, Transportation Tags , , ,

    Hayrapetyan, Tardos and Wexler recently introduced a framework to study the impact of collusion in congestion games on the quality of Nash equilibria. We adopt their framework to network games and focus on the well established price of anarchy as a measure of this impact. We first investigate nonatomic network games with coalitions. For this … Read more