R. Horst

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In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D. C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P. M. Pardalos and N. V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu­ merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di­ verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith­ mic, and computational contributions have helped to solve globally multi­ extreme problems arising from important practical applications.

In this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D. C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P. M. Pardalos and N. V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu­ merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di­ verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith­ mic, and computational contributions have helped to solve globally multi­ extreme problems arising from important practical applications.

Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications. Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved. Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering.

Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications. Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved. Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering.