The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo rithms, are gaining in popularity among practitioners and engineers be they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems. However, the theoretical performance of these stochastic methods is not well under stood. In this book, an attempt is made to describe the theoretical prop erties of several stochastic adaptive search methods. Such a theoretical understanding may allow us to better predict algorithm performance and ultimately design new and improved algorithms. This book consolidates a collection of papers on the analysis and de velopment of stochastic adaptive search. The first chapter introduces random search algorithms. Chapters 2-5 describe the theoretical anal ysis of a progression of algorithms. A main result is that the expected number of iterations for pure adaptive search is linear in dimension for a class of Lipschitz global optimization problems. Chapter 6 discusses algorithms, based on the Hit-and-Run sampling method, that have been developed to approximate the ideal performance of pure random search. The final chapter discusses several applications in engineering that use stochastic adaptive search methods.

This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.

Papers from the April 1995 title conference, held at Princeton University, present current research on global optimization and related applications in science and engineering, highlighting the use of new algorithms for solving large classes of problems in areas such as computational chemistry and biology, structural optimization, and operations research. Topics include Lagrange duality in partly convex programming, global optimization using hyperbolic cross points, and adaptive control via non-convex optimization. Of interest to students and researchers in optimization, engineering, mathematics, and computer sciences. No index. Annotation copyright by Book News, Inc., Portland, OR

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.