Optimization on Low Rank Nonconvex Structures / Edition 1

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Overview

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.

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Editorial Reviews

From the Publisher
'Overall this is a book which can be recommended to anyone who wishes to know more about the incrteasingly important area of global optimization.'
Mathematical Reviews, 98i
Booknews
In light of recent advances made possible by the emergence of inexpensive personal computers and powerful workstations, and the large number of quite efficient deterministic algorithms that have been proposed over the past decade, examines the latest methods for solving global optimization problems with special structures, most of them highly non-convex but amenable to becoming convex when a few variables are fixed. Covers the fundamental concepts and principles, numerical methods and algorithms for solving typical classes of global optimization problems, and selected applications in engineering and economics. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

Table of Contents

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.

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