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Convex Analysis and Global Optimization de Hoang Tuy

Convex Analysis and Global Optimization: Nonconvex Optimization and Its Applications, cartea 22

Autor Hoang Tuy
en Limba Engleză Paperback – 6 dec 2010
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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Specificații

ISBN-13: 9781441947833
ISBN-10: 1441947833
Pagini: 352
Ilustrații: XII, 340 p.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.5 kg
Ediția:Softcover reprint of hardcover 1st ed. 1998
Editura: Springer Us
Colecția Springer
Seria Nonconvex Optimization and Its Applications

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

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

Recenzii

`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)

Textul de pe ultima copertă

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 basisand 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)

Caracteristici

Presents up-to-date research and methodologies in modern global optimization Serves as a reference for a wide swath of the optimization community Equips readers to handle a mathematically rigorous approach to modern global optimization and its potential applications Covers fundamental concepts, theoretical foundations and practical implementation of algorithms Includes supplementary material: sn.pub/extras