Aspects of Semidefinite Programming, E. de Klerk

Автор: Anjos
Название: Handbook on Semidefinite, Conic and Polynomial Optimization
ISBN: 1461407680 ISBN-13(EAN): 9781461407683
Издательство: Springer
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Описание: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts:Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;Algorithms, documenting the directions of current algorithmic development;Software, providing an overview of the state-of-the-art;Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Автор: Henry Wolkowicz; Romesh Saigal; Lieven Vandenbergh
Название: Handbook of Semidefinite Programming
ISBN: 1461369703 ISBN-13(EAN): 9781461369707
Издательство: Springer
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Цена: 27950.00 р.
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Описание: This handbook offers a broad, advanced overview of the current state of Semidefinite Programming, in nineteen chapters written by the leading experts on the subject. The material is organized in three parts: Theory, Algorithms, and Applications and Extensions.

Автор: Miguel F. Anjos; Jean B. Lasserre
Название: Handbook on Semidefinite, Conic and Polynomial Optimization
ISBN: 1489978038 ISBN-13(EAN): 9781489978035
Издательство: Springer
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Цена: 33401.00 р.
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Описание: This book offers the reader a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization and polynomial optimization. It covers theory, algorithms, software and applications.

Автор: G?rtner, Matousek
Название: Approximation Algorithms and Semidefinite Programming
ISBN: 3642220142 ISBN-13(EAN): 9783642220142
Издательство: Springer
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Цена: 9781.00 р.
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Описание: Semidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.  There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms. This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.