Global optimization is one of the fastest developing fields in mathematical optimization. In fact, an increasing number of remarkably efficient deterministic algorithms have been proposed in the last ten years for solving several classes of large scale specially structured problems encountered in such areas as chemical engineering, financial engineering, location and network optimization, production and inventory control, engineering design, computational geometry, and multi-objective and multi-level optimization. These new developments motivated the authors to write a new book devoted to global optimization problems with special structures. Most of these problems, though highly nonconvex, can be characterized by the property that they reduce to convex minimization problems when some of the variables are fixed. A number of recently developed algorithms have been proved surprisingly efficient for handling typical classes of problems exhibiting such structures, namely low rank nonconvex structures. Audience: The book will serve as a fundamental reference book for all those who are interested in mathematical optimization.

Inhalt

Preface. Part I: Foundations. 1. Scope of Global Optimization. 2. Quasi-Convexity. 3. D.C. Functions and D.C. Sets. 4. Duality. 5. Low-Rank Nonconvex Structures. 6. Global Search Methods and Basic D.C. Optimization Algorithms. Part II: Methods and Algorithms. 7. Parametric Approaches in Global Optimization. 8. Multiplicative Programming Problems. 9. Monotonic Problems. 10. Decomposition Methods by Prices. 11. Dynamic Programming Algorithms in Global Optimization. Part III: Selected Applications. 12. Low Rank Nonconvex Quadratic Programming. 13. Continuous Location. 14. Design Centering and Related Geometric Problems. 15. Multiobjective and Bilevel Programming. References. Index.