Convex Analysis and Global Optimization, 2nd Edition

Authors: Hoang Tuy



Presents up-to-date research and methodologies in modern global optimization

Serves as a reference for a wide swath of the optimization community

Equips readers to handle a mathematically rigorous approach to modern global optimization and its potential applications

Covers fundamental concepts, theoretical foundations and practical implementation of algorithms

This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come.

Updates for this new edition include:
· Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization;
· Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints;
· Important discussions of decomposition methods for specially structured problems;
· A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition.
· Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint.

Table of contents

Front Matter
Pages i-xvi

Convex Analysis
Front Matter
Pages 1-1

Convex Sets
Pages 3-37

Convex Functions
Pages 39-86

Fixed Point and Equilibrium
Pages 87-102

DC Functions and DC Sets
Pages 103-123

Global Optimization
Front Matter
Pages 125-125

Motivation and Overview
Pages 127-149

General Methods
Pages 151-165

DC Optimization Problems
Pages 167-228

Special Methods
Pages 229-281

Parametric Decomposition
Pages 283-336

Nonconvex Quadratic Programming
Pages 337-390

Monotonic Optimization
Pages 391-433

Polynomial Optimization
Pages 435-452

Optimization Under Equilibrium Constraints
Pages 453-487

Back Matter
Pages 489-505

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