Описание: Over the past two decades there have been significant advances in the field of optimization. In particular, convex optimization has emerged as a powerful signal processing tool, and the variety of applications continues to grow rapidly. This book, written by a team of leading experts, sets out the theoretical underpinnings of the subject and provides tutorials on a wide range of convex optimization applications. Emphasis throughout is on cutting-edge research and on formulating problems in convex form, making this an ideal textbook for advanced graduate courses and a useful self-study guide. Topics covered range from automatic code generation, graphical models, and gradient-based algorithms for signal recovery, to semidefinite programming (SDP) relaxation and radar waveform design via SDP. It also includes blind source separation for image processing, robust broadband beamforming, distributed multi-agent optimization for networked systems, cognitive radio systems via game theory, and the variational inequality approach for Nash equilibrium solutions.
Автор: Stephen Boyd Название: Convex Optimization ISBN: 0521833787 ISBN-13(EAN): 9780521833783 Издательство: Cambridge Academ Рейтинг: Цена: 8221 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Автор: Sundaram, Rangarajan K. Название: A First Course in Optimization Theory ISBN: 0521497701 ISBN-13(EAN): 9780521497701 Издательство: Cambridge Academ Рейтинг: Цена: 3642 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces students to optimization theory and its use in economics and allied disciplines.
Автор: Bot, Radu Ioan Название: Conjugate duality in convex optimization ISBN: 3642048994 ISBN-13(EAN): 9783642048999 Издательство: Springer Рейтинг: Цена: 9817 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: New findings in the theory of conjugate duality for convex optimization problems are presented in this comprehensive review. The formulation of generalized Moreau-Rockafellar formulae, play a central role in the book, which constitute a new class of regularity conditions.
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.
Описание: The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the RГҐdstrГ¶m-HГ¶rmander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity.In the first three chapters of the book the basic facts about convexity, mixed volumes and the RГҐdstrГ¶m-HГ¶rmander lattice are presented. Then, a comprehensive theory on inclusion-minimal representants of pairs of compact convex sets is given. Special attention is given to the two-dimensional case, where the minimal pairs are uniquely determined up to translations. This fact is not true in higher dimensional spaces and leads to a beautiful theory on the mutual interactions between minimality under constraints, separation and decomposition of convex sets, convexificators and invariants of minimal pairs. This theory throws light upon both sides of the collection of all compact convex subsets of a locally vector space, namely the geometric and the algebraic one.From the algebraic point of view the collection of all nonempty compact convex subsets of a topological vector space is an ordered semi group with cancellation property under the inclusion of sets and the Minkowski-addition. From this approach pairs of nonempty compact convex sets correspond to fractions of elements from the semi group and minimal pairs to relatively prime fractions.
Описание: This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.
Описание: This volume provides a systematic examination of Lagrange-type functions and augmented Lagrangians. Weak duality, zero duality gap property and the existence of an exact penalty parameter are examined. Weak duality allows one to estimate a global minimum. The zero duality gap property allows one to reduce the constrained optimization problem to a sequence of unconstrained problems, and the existence of an exact penalty parameter allows one to solve only one unconstrained problem. By applying Lagrange-type functions, a zero duality gap property for nonconvex constrained optimization problems is established under a coercive condition. It is shown that the zero duality gap property is equivalent to the lower semi-continuity of a perturbation function. In particular, for a type of kth power penalty functions, this book obtains an analytic expression of the least exact penalty parameter and establishes that a fairly small exact penalty parameter can be achieved. As shown by numerical experiments, this property is very important for some global methods of Lipschitz programming, otherwise ill conditioning may occur. Audience: The book is suitable for researchers in mathematical programming and optimization and postgraduate students in applied mathematics.
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: Borwein Название: Convex Analysis and Nonlinear Optimization ISBN: 0387295704 ISBN-13(EAN): 9780387295701 Издательство: Springer Рейтинг: Цена: 5605 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Optimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained.
Описание: This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or their extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A distinct primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. Exemplary applications are studied to assess the performance of the theoretical concepts in situations of practical relevance. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can typically be reduced to a few percent at reasonable problem dimensions.
Описание: This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306), which presented an introduction to the basic concepts in convex analysis and a study of convex minimization problems. The "backbone" of both volumes was extracted, some material deleted that was deemed too advanced for an introduction, or too closely related to numerical algorithms. Some exercises were included and finally the index has been considerably enriched. The main motivation of the authors was to "light the entrance" of the monument Convex Analysis. This book is not a reference book to be kept on the shelf by experts who already know the building and can find their way through it; it is far more a book for the purpose of learning and teaching.
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