Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.

Inhalt

Part I: Convex Analysis. 1. Convex Sets. 2. Convex Functions. 3. D.C. Functions and D.C. Sets. Part II: Global Optimization. 4. Motivation and Overview. 5. Successive Partitioning Methods. 6. Outer and Inner Approximation. 7. Decomposition. 8. Nonconvex Quadratic Programming. References. Index.