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Modern Optimization Modelling Techniques

  • Roberto Cominetti
  • Francisco Facchinei
  • Jean B. Lasserre

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Moments and Positive Polynomials for Optimization

    1. Front Matter
      Pages 1-5
    2. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 7-27
    3. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 29-46
    4. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 47-79
    5. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 81-92
    6. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 93-120
    7. Back Matter
      Pages 121-130
  3. Computation of Generalized Nash Equilibria: Recent Advancements

    1. Front Matter
      Pages 131-143
    2. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 145-149
    3. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 151-162
    4. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 163-173
    5. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 175-188
    6. Back Matter
      Pages 189-204
  4. Equilibrium and Learning in Traffic Networks

    1. Front Matter
      Pages 205-211
    2. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 213-220
    3. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 221-238
    4. Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
      Pages 239-257
    5. Back Matter
      Pages 259-269

About this book

Introduction

This book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009.

The theory of optimization, understood in a broad sense, is the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations (structure, stability) to applied operational research and engineering applications. The compiled material of this book puts on display this versatility, by exhibiting the three parallel and complementary components of optimization: theory, algorithms, and practical problems.

The first part is a self-contained course on the general moment problem and its relations with semidefinite programming. The second part is dedicated to the problem of determination of Nash equilibria from an algorithmic viewpoint. The last part presents congestion models for traffic networks and develops modern optimization techniques for finding traffic equilibria based on stochastic optimization and game theory.

Keywords

Nash equilibrium learning moment problems polynomial optimization traffic networks

Authors and affiliations

  • Roberto Cominetti
    • 1
  • Francisco Facchinei
    • 2
  • Jean B. Lasserre
    • 3
  1. 1., Departamento de Ingeniería IndustrialUniversidad de ChileSantiago de ChileChile
  2. 2., Dept. Computer, Control, Manag. Eng.Università di Roma "La Sapienza"RomaItaly
  3. 3.LAAS-CNRSToulouse Cedex 4France

Bibliographic information