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 book contains an expanded version of three series of lectures delivered by the authors at the CRM in July 2009. 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.
Author(s): Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre (auth.)
Series: Advanced Courses in Mathematics - CRM Barcelona
Edition: 1
Publisher: Birkhäuser Basel
Year: 2012
Language: English
Pages: 269
Tags: Operations Research, Management Science; Game Theory, Economics, Social and Behav. Sciences
Front Matter....Pages i-ix
Front Matter....Pages 1-5
Chapter 1 Representation of Positive Polynomials....Pages 7-27
Chapter 2 Moments....Pages 29-46
Chapter 3 Polynomial Optimization....Pages 47-79
Chapter 4 Convexity in Polynomial Optimization....Pages 81-92
Chapter 5 Parametric Polynomial Optimization....Pages 93-120
Back Matter....Pages 121-130
Front Matter....Pages 131-143
Chapter 1 Some Telecommunication Applications....Pages 145-149
Chapter 2 NEPs and Jointly Convex GNEPs....Pages 151-162
Chapter 3 Jointly Convex Nash Equilibrium Problems....Pages 163-173
Chapter 4 GNEPs with No Special Structure....Pages 175-188
Back Matter....Pages 189-204
Front Matter....Pages 205-211
Chapter 1 Wardrop and Stochastic User Equilibrium....Pages 213-220
Chapter 2 Markovian Traffic Equilibrium....Pages 221-238
Chapter 3 Adaptive Dynamics in Traffic Games....Pages 239-257
Back Matter....Pages 259-269
