Handbook on Semidefinite, Conic and Polynomial Optimization,

Старое издание

Автор: Anjos Название: Handbook on Semidefinite, Conic and Polynomial Optimization ISBN: 1461407680 ISBN-13(EAN): 9781461407683 Издательство: Springer Цена: 22347 р. Наличие на складе: Есть (1 шт.) 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: Anjos Название: Handbook on Semidefinite, Conic and Polynomial Optimization ISBN: 1461407680 ISBN-13(EAN): 9781461407683 Издательство: Springer Рейтинг: Цена: 22347 р. Наличие на складе: Есть (1 шт.) 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: Wolkowicz Название: Handbook of Semidefinite Programming ISBN: 0792377710 ISBN-13(EAN): 9780792377719 Издательство: Springer Рейтинг: Цена: 27957 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very
diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research
activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the
development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory.

"The Handbook of Semidefinite
Programming" offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are
organized in three parts: Theory, Algorithms, and Applications and Extensions.

Автор: Li Название: Approximation Methods for Polynomial Optimization ISBN: 1461439833 ISBN-13(EAN): 9781461439837 Издательство: Springer Цена: 4670 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: Polynomial optimization have been a hot research topic for the past few years and its applications range from Operations Research, biomedical engineering, investment science, to quantum mechanics, linear algebra, and signal processing, among many others. In this brief the authors discuss some important subclasses of polynomial optimization models arising from various applications, with a focus on approximations algorithms with guaranteed worst case performance analysis. The brief presents a clear view of the basic ideas underlying the design of such algorithms and the benefits are highlighted by illustrative examples showing the possible applications. This timely treatise will appeal to researchers and graduate students in the fields of optimization, computational mathematics, Operations Research, industrial engineering, and computer science.

Автор: Stout Edgar Lee Название: Polynomial Convexity ISBN: 0817645373 ISBN-13(EAN): 9780817645373 Издательство: Springer Рейтинг: Цена: 12154 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables.Important features of Polynomial Convexity:*Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets.*Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.*Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation on noncompact sets.*Discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions.*Requires of the reader a solid background in real and complex analysis together with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis. This beautiful exposition of a rich and complex theory, which contains much material not available in other texts, is destined to be the standard reference for many years, and will appeal to all those with an interest in multivariate complex analysis.

Описание: This book provides a self-contained, accessible introduction to the mathematical advances and challenges resulting from the use of semidefinite programming in polynomial optimization. This important and highly applicable research area, with contributions from convex geometry, algebraic geometry and optimization, is known as convex algebraic geometry. Each chapter addresses a fundamental aspect of the topic, beginning with an introduction to nonnegative polynomials and sums of squares, and their connections to semidefinite programming. The material quickly advances to areas at the forefront of current research, including semidefinite representability of convex sets, duality theory in algebraic geometry, and nontraditional topics such as sums of squares of complex forms. The book is a suitable entry point to the subject for readers at the graduate level or above in mathematics, engineering or computer science. Instructors will find the book appropriate for a class or seminar, and researchers will encounter open problems and new research directions.

Описание: Semidefinite programming has been described as linear programming for the year 2000. It is an exciting new branch of mathematical programming, due to important applications in control theory, combinatorial optimization and other fields. 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. This includes the latest results on the properties of the central path as well as the analysis of the most important classes of algorithms. Several "classic" applications of semidefinite programming are also described in detail. These include the LovГЎsz theta function and the MAX-CUT approximation algorithm by Goemans and Williamson. Audience: Researchers or graduate students in optimization or related fields, who wish to learn more about the theory and applications of semidefinite programming.

Автор: G?rtner, Matousek Название: Approximation Algorithms and Semidefinite Programming ISBN: 3642220142 ISBN-13(EAN): 9783642220142 Издательство: Springer Рейтинг: Цена: 6544 р. Наличие на складе: Есть у поставщика Поставка под заказ.

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: Borwein Название: Polynomials and Polynomial Inequalities ISBN: 0387945091 ISBN-13(EAN): 9780387945095 Издательство: Springer Рейтинг: Цена: 5886 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: The material explored in this text primarily concerns polynomials and rational functions of a single variable. Appendices on algorithms and computational concerns on the interpolation theorem, and on orthogonality and irrationality conclude the discussion.

Описание: This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.

Описание: This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.

Автор: Vui Ha Huy Et Al Название: Genericity In Polynomial Optimization ISBN: 1786342219 ISBN-13(EAN): 9781786342218 Издательство: World Scientific Publishing Цена: 8864 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание:

In full generality, minimizing a polynomial function over a closed semi-algebraic set requires complex mathematical equations. This book explains recent developments from singularity theory and semi-algebraic geometry for studying polynomial optimization problems. Classes of generic problems are defined in a simple and elegant manner by using only the two basic (and relatively simple) notions of Newton polyhedron and non-degeneracy conditions associated with a given polynomial optimization problem. These conditions are well known in singularity theory, however, they are rarely considered within the optimization community.

Explanations focus on critical points and tangencies of polynomial optimization, HOlderian error bounds for polynomial systems, Frank-Wolfe-type theorem for polynomial programs and well-posedness in polynomial optimization. It then goes on to look at optimization for the different types of polynomials. Through this text graduate students, PhD students and researchers of mathematics will be provided with the knowledge necessary to use semi-algebraic geometry in optimization.

Название: Handbook Of The Tutte Polynomial ISBN: 1482240629 ISBN-13(EAN): 9781482240627 Издательство: Taylor&Francis Цена: 13585 р. Наличие на складе: Поставка под заказ.

Описание:

It has become a well-known fact that most graph polynomials are related to the Tutte Polynomial in some way. In fact, that area of graph polynomials has grown to such an extent that it now has its own subject classification (05C31). This handbook is the first one published on the Tutte Polynomial which is a central, heavily-studied object in the field of combinatorics with applications in a wide range of other fields such as geometry, biology and physics.

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