Convex Analysis and Global Optimization

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Focusing on the essential role of convex analysis in nonconvex optimization, this book presents a comprehensive theory of deterministic global optimization. The first part introduces key concepts and properties of convex analysis relevant to global optimization, particularly the complementary convex structure. The second part explores global search principles, including partitioning, approximation methods, and decomposition techniques, applied to various optimization challenges, including low-rank nonconvex and quadratic problems, while introducing significant new material.