Global Optimization : Deterministic Approaches

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.

The new edition contains modifications and additions which take into account recent developments in the field.
From the reviews of earlier editions:
"The book is clearly written and lucidly structured. In particular, the used notations are thoroughly defined, the diverse ideas are well explained, and the results are beautifully motivated." (ZOR. Methods and Models of Operations Research).
This book develops a systematic and unifying approach to the most important classes of constrained global optimization and their solution techniques. The main problem classes treated are concave minimization, reverse convex and d. c. programming, Lipschitz and continuous optimization, and systems of equations and inequalities.

Front Matter....Pages I-XVIII Front Matter....Pages 1-1 Some Important Classes of Global Optimization Problems....Pages 3-51 Outer Approximation....Pages 53-87 Concavity Cuts....Pages 89-114 Branch and Bound....Pages 115-178 Front Matter....Pages 179-179 Cutting Methods....Pages 181-224 Successive Approximation Methods....Pages 225-293 Successive Partition Methods....Pages 295-380 Decomposition of Large Scale Problems....Pages 381-446 Special Problems of Concave Minimization....Pages 447-515 Front Matter....Pages 517-517 D.C. Programming....Pages 519-601 Lipschitz and Continuous Optimization....Pages 603-679 Back Matter....Pages 681-729