Автор: Blekherman Название: Semidefinite Optimization and Convex Algebraic Geometry ISBN: 1611972280 ISBN-13(EAN): 9781611972283 Издательство: Eurospan Рейтинг: Цена: 198630 T Наличие на складе: Невозможна поставка. 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.
Автор: de Klerk E. Название: Aspects of Semidefinite Programming / Interior Point Algorithms and Selected Applications ISBN: 1402005474 ISBN-13(EAN): 9781402005473 Издательство: Springer Рейтинг: Цена: 196290 T Наличие на складе: Поставка под заказ. 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: Dumitrescu B. Название: Positive Trigonometric Polynomials and Signal Processing Applications ISBN: 1402051247 ISBN-13(EAN): 9781402051241 Издательство: Springer Рейтинг: Цена: 173240 T Наличие на складе: Поставка под заказ. Описание: Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications.
Автор: Lasserre Название: An Introduction to Polynomial and Semi-Algebraic Optimization ISBN: 110763069X ISBN-13(EAN): 9781107630697 Издательство: Cambridge Academ Рейтинг: Цена: 54770 T Наличие на складе: Поставка под заказ. 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: Lasserre Название: An Introduction to Polynomial and Semi-Algebraic Optimization ISBN: 1107060575 ISBN-13(EAN): 9781107060579 Издательство: Cambridge Academ Рейтинг: Цена: 158860 T Наличие на складе: Поставка под заказ. 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: Nesterov Название: Interior Point Polynomial Algorithms in Convex Programming ISBN: 0898715156 ISBN-13(EAN): 9780898715156 Издательство: Eurospan Рейтинг: Цена: 159760 T Наличие на складе: Поставка под заказ. Описание: Written for specialists working in optimization, mathematical programming, or control theory. The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered. In this book, the authors describe the first unified theory of polynomial-time interior-point methods. Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs.
Автор: Lasserre, Jean-bernard Название: Moments, positive polynomials and their applications ISBN: 1848164459 ISBN-13(EAN): 9781848164451 Издательство: World Scientific Publishing Рейтинг: Цена: 138320 T Наличие на складе: Поставка под заказ. Описание: Many important problems in global optimization, algebra, probability and statistics, applied mathematics, control theory, and financial mathematics can be modeled as a particular instance of the Generalized Moment Problem (GMP). This book introduces a general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets.
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