Hoang Tuy

Convex Analysis and Global Optimization (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 340
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9781475728095
• Artikelnr.: 44064473

Inhaltsangabe

1. Convex Sets.- 2. Convex Functions.- 3. Fixed Point and Equilibrium.- 4. DC Functions and DC Sets.- 5. Motivation and Overview.- 6. General Methods.- 7. DC Optimization Problems.- 8. Special Methods.- 9. Parametric Decomposition.- 10. Nonconvex Quadratic Programming.- 11. Monotonic Optimization.- 12. Polynomial Optimization.- 13. Optimization Under Equilibrium Constraints.- References.- Index.

Rezensionen

"This is a very pleasant text on global optimization problems, concentrating on those problems that have some kind of convexity property. It describes itself as a Ph.D. level text, but in fact it is easy to read and develops all the necessary background, so it could be used by any sufficiently-motivated student. ... Each chapter has a good selection of problems, both proof problems and specific problems to optimize." (Allen Stenger, MAA Reviews, July, 2017)

"This reviewer believes that the book can be recommended not only to researchers but also to graduate students ... and even practioners, who can identify problems arising from various fields among those dealt with in the book." (Sorin-Mihai Grad,Mathematical Reviews, June, 2017)

"The book is a well-prepared exposition of the state-of-the-art of the theory and algorithms in the area of modern global optimization. ... a good choice if one needs a textbook for graduate or PhD course. It would be also suitable for engineers and other practitionners that would like to better understand the algorithms that they use." (Marcin Anholcer, zbMATH 1362.90001, 2017)

`The book gives a good review of the topic. ... The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.' Mathematical Methods of Operations Research, 49:3 (1999)