Handbook on Semidefinite, Conic and Polynomial Optimization, Miguel F. Anjos; Jean B. Lasserre

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: 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.

Автор: Graziano Chesi; Andrea Garulli; Alberto Tesi; Anto
Название: Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems
ISBN: 1848827806 ISBN-13(EAN): 9781848827806
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This book presents a number of techniques for robustness analysis of uncertain systems. In it, convex relaxations for several robustness problems are derived by exploiting and providing new results on the theory of homogenous polynomial forms.

Автор: E. de Klerk
Название: Aspects of Semidefinite Programming
ISBN: 1441952160 ISBN-13(EAN): 9781441952165
Издательство: Springer
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Описание: Semidefinite programming has been described as linear programming for the year 2000. Moreover, the successful interior point algorithms for linear programming can be extended to semidefinite programming.In this monograph the basic theory of interior point algorithms is explained.

Автор: N.Z. Shor
Название: Nondifferentiable Optimization and Polynomial Problems
ISBN: 0792349970 ISBN-13(EAN): 9780792349976
Издательство: Springer
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Цена: 27245.00 р.
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Описание: This work is devoted to an investigation of polynomial optimization problems, including Boolean problems which are the most important part of mathematical programming. It demonstrates methods of nondifferentiable optimization that can be used for finding solutions to many polynomial problems.

Автор: Alicia Dickenstein; Ioannis Z. Emiris
Название: Solving Polynomial Equations
ISBN: 3642063616 ISBN-13(EAN): 9783642063619
Издательство: Springer
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Цена: 12571.00 р.
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Автор: Teo Mora
Название: Solving Polynomial Equation Systems I
ISBN: 0521811546 ISBN-13(EAN): 9780521811545
Издательство: Cambridge Academ
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Описание: Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.