Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications

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This title provides a comprehensive treatment of convexification and global optimization of continuous and mixed-integer nonlinear programs. Developed for students, researchers, and practitioners, the book covers theory, algorithms, software, and applications. The book: develops a powerful and widely applicable framework for constructing closed-form expressions of convex envelopes of nonlinear functions; presents a systematic treatment of branch-and-bound, while providing acceleration mechanisms and enhancements; unifies ideas at the interface between operations research and computer science, devising efficient algorithmic implementation for global optimization; offers students, modellers, and algorithm developers a rich collection of models, applications, and numerical examples; elucidates through geometric interpretations the concepts discussed throughout the book; shows how optimization theory can lead to breakthroughs in diverse application areas, including molecular design, process and product design, facility location, and supply chain design and operation; and demonstrates that the BARON software developed by the authors can solve global optimization problems heretofore considered intractable, in an entirely automated manner on a personal computer.