Hoàng Tụy Bücher

This book presents cutting-edge results and methodologies in global optimization, serving as a key reference for researchers, engineers, advanced students, and practitioners across various engineering fields. The updated second edition enhances the coherent and rigorous theory of deterministic global optimization, emphasizing the importance of convex analysis. It has been revised and expanded to address the evolving needs of research, education, and applications for years to come. Key updates include discussions on modern approaches to minimax, fixed point, and equilibrium theorems, as well as nonconvex optimization. The text places greater emphasis on efficiently tackling ill-posed global optimization problems, particularly those with hard constraints. It also features important discussions on decomposition methods for specially structured problems and a complete revision of the chapter on nonconvex quadratic programming, reflecting recent advances in the field. New chapters are dedicated to monotonic optimization, polynomial optimization, and optimization under equilibrium constraints, including bilevel and multiobjective programming, as well as optimization with variational inequality constraints. Reviews of the first edition noted its clear exposition and comprehensive coverage, making it a valuable resource for both students and professionals in the field.

The main contents and character of the monograph did not change with respect to the first edition. However, within most chapters we incorporated quite a number of modifications which take into account the recent development of the field, the very valuable suggestions and comments that we received from numerous colleagues and students as well as our own experience while using the book. Some errors and misprints in the first edition are also corrected. Reiner Horst May 1992 Hoang Tuy PREFACE TO THE FIRST EDITION The enormous practical need for solving global optimization problems coupled with a rapidly advancing computer technology has allowed one to consider problems which a few years aga would have been considered computationally intractable. As a consequence, we are seeing the creation of a large and increasing number of diverse algorithms for solving a wide variety of multiextremal global optimization problems. The goal of this book is to systematically clarify and unify these diverse approaches in order to provide insight into the underlying concepts and their pro perties. Aside from a coherent view of the field much new material is presented.