ADVANCED COURSES IN MATHEMATICS CRM BARCELONA

Opis produktu

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 selfcontained 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 tThis 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 engineeriPart 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 RoThis 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 selfcontained 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 tMost 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 relevanceto illustrate the theory/Applications of much practical relevanceto illustrate the theoryNumerous results and exampleshighlight the close connection of optimization theory with other related fields such as dynamical syst

Wymiary: 168 mm 240 mm