Convex Analysis and Global Optimization

ISBN-13: 9783319810492 / Angielski / Miękka / 2018 / 505 str.

Hoang Tuy

Recenzje

"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)

Spis treści

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. 

Blurb

This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come.

Updates for this new edition include:

·        Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization;

·        Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints;

·        Important discussions of decomposition methods for specially structured problems;

·        A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition.

·        Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint.

From the reviews of the first edition:

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)