Hoang Tuy Knihy

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.

Focused on global optimization, this monograph addresses the practical need for solving complex problems enhanced by advancements in computer technology. It presents a unified framework for various algorithms developed for multiextremal global optimization, aiming to clarify their underlying concepts and properties. The updated edition incorporates modifications based on feedback from colleagues and students, as well as corrections of previous errors, ensuring a comprehensive and insightful resource for readers interested in the evolving field.