This book covers the theory of optimization, understood as the basis of modern applied mathematics, covering a large spectrum of topics from theoretical considerations to applied operational research and engineering applications.

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.

Most of the material covered in the book concerns results that so far were only available as articles in specialized journals Provides a comprehensive overview of the recent developments and makes them accessible to a wider audience, including graduate students and researchers interested in the broad field of optimization Applications of much practical relevance to illustrate the theory Numerous results and examples highlight the close connection of optimization theory with other related fields such as dynamical systems, equilibrium theory, stochastic modeling, game theory, etc. Includes supplementary material: sn.pub/extras

Klappentext
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.

Inhalt
Part I: Moments and Positive Polynomials for Optimization by Jean B. Lasserre.- Part II: Computation of Generalized Nash Equilibria: Recent Advancements by Francisco Facchinei.- Part III: Equilibrium and Learning in Traffic Networks by Roberto Cominetti.