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."

This volume is a collection of papers presented at the Eighth French-German Conference on Optimization held at the University of Trier (Germany) in 1996. From July 21 through July 26, 1996, about 100 scientists, mainly from France and Germany, but also from other countries, met at Trier to discuss recent de- velopments in the field of optimization. 89 lectures were delivered, covering a large range of theoretical and practical aspects of optimization. Most of the talks were scheduled in two parallel sessions, grouped into sections including convex and nonsmooth analysis, methods in convex and nonconvex program- ming, sensitivity and stability analysis, control theory, ill-posed programming problems, equilibrium problems, and global optimization. Continuing an old tradition, the Eighth French-German Conference on Opti- mization demonstrated vividly the vitality of the French-German cooperation in mathematics. The Scientific Committee of the conference consisted of A. Auslender (Paris), H.G. Bock (Heidelberg), S. Dolecki (Dijon), R. Durier (Dijon), J.B. Hiriart- Urruty (Toulouse), H. Th. Jongen (Aachen), D. Klatte (Zurich), B. Kum- mer (Berlin), C. Lemarechal (Rocquencourt), P. Loridan (Paris), C. Mich- elot (Dijon), W. Oettli (Mannheim), D. Pallaschke (Karlsruhe), J.P. Penot (Pau), J. Stoer (Wurzburg), M. Thera (Limoges), L. Thibault (Montpellier), R. Tichatschke (Trier)' J. Zowe (Erlangen).

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."

Global optimization is concerned with the computation and characterization of global optima of nonlinear functions. During the past three decades the field of global optimization has been growing at a rapid pace, and the number of publications on all aspects of global optimization has been increasing steadily. Many applications, as well as new theoretical, algorithmic, and computational contributions have resulted. The Handbook of Global Optimization is the first comprehensive book to cover recent developments in global optimization. Each contribution in the Handbook is essentially expository in nature, but scholarly in its treatment. The chapters cover optimality conditions, complexity results, concave minimization, DC programming, general quadratic programming, nonlinear complementarity, minimax problems, multiplicative programming, Lipschitz optimization, fractional programming, network problems, trajectory methods, homotopy methods, interval methods, and stochastic approaches. The Handbook of Global Optimization is addressed to researchers in mathematical programming, as well as all scientists who use optimization methods to model and solve problems.

th The purpose of this volume is to reflect the scientific activities during the 16 Sym- posium on Operations Research which took place at the University of Trier from September 9 through September 11, 1991. The Symposia on Operations Research are the annual conferences of the Gesellschaft fur Mathematik, Okonomie und Operations Research (GMOOR). This so- ciety which was founded in 1977 pursues the goal to support and facilitate research, development, application and education in an area where mathematics, economICS, operations research, computer science and system theory come together. th The 16 ' Symposium on Operations Research stood under t.he auspices of the Minister- priisident of the state of Rheinland-Pfalz, Rudolf Scharping. The opening addresses were given by the president of the Universitiit Trier, Professor Hasler, by the Minister fur Wissenschaft und Weiterbildung, Professor Zollner, and by Professor Hettich, on behalf of the organizers. These addresses are printed as part of the introductory material of this volume. The conference was attended by 351 participants from 29 countries; more than 70% of the participants gave lectures on their current res each interests, surveys on spe- cial topics or software demonstrations. They made the meeting truely a successful international forum for scientific exchange. The conference was highlighted by the award of the society's scientific prize in memo- riam Rudolf Henn to Professor R.E. Burkard, Technical University Graz, and his plenary GMOOR-Award winner lecture on Convexity and Discrete Optimization.