Convex Analysis and Global Optimization

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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 disciplines. The second edition has been updated to enhance a coherent and rigorous theory of deterministic global optimization, emphasizing the importance of convex analysis. It has been revised to address the needs of research, education, and applications for the future. Key updates include discussions on modern approaches to minimax, fixed point, equilibrium theorems, and nonconvex optimization, with a focus on efficiently addressing ill-posed global optimization problems, especially those with hard constraints. The chapter on nonconvex quadratic programming has been thoroughly revised to reflect advancements in the field since the first edition. New chapters have been added on monotonic optimization, polynomial optimization, and optimization under equilibrium constraints, covering bilevel programming, multiobjective programming, and optimization with variational inequality constraints. The first edition received praise for its clear exposition and comprehensive review of global optimization concepts, making it a valuable resource for both students and professionals.