Introductory Lectures on Convex Optimization / A Basic Course, Nesterov Y.
Автор: Stephen Boyd Название: Convex Optimization ISBN: 0521833787 ISBN-13(EAN): 9780521833783 Издательство: Cambridge Academ Рейтинг: Цена: 10955 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.
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.
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.
Автор: Bot, Radu Ioan Название: Conjugate duality in convex optimization ISBN: 3642048994 ISBN-13(EAN): 9783642048999 Издательство: Springer Рейтинг: Цена: 12126 р. Наличие на складе: 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: 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: 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.
Автор: Florenzano Monique, Le Van Cuong, Gourdel P. Название: Finite Dimensional Convexity and Optimization ISBN: 3540415165 ISBN-13(EAN): 9783540415169 Издательство: Springer Рейтинг: Цена: 15014 р. Наличие на складе: Поставка под заказ.
Описание: The primary aim of this book is to present notions of convex analysis which constitute the basic underlying structure of argumentation in economic theory and which are common to optimization problems encountered in many applications. The intended readers are graduate students, and specialists of mathematical programming whose research fields are applied mathematics and economics. The text consists of a systematic development in eight chapters, with guided exercises containing sometimes significant and useful additional results. The book is appropriate as a class text, or for self-study.
Автор: Leonard D. Berkovitz Название: Convexity and Optimization in Rn ISBN: 0471352810 ISBN-13(EAN): 9780471352815 Издательство: Wiley Рейтинг: Цена: 21581 р. Наличие на складе: Поставка под заказ.
Описание: This book presents the mathematics of finitimensional constrained optimization problems. It offers a solid presentation of real analysis and provides a basis for the mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems.
Описание: This book presents basic optimization principles and gradient-based algorithms to a general audience in a brief and easy-to-read form, without neglecting rigor. The work should enable professionals to apply optimization theory and algorithms to their own particular practical fields of interest, be it engineering, physics, chemistry, or business economics. Most importantly, for the first time in a relatively brief and introductory work, due attention is paid to the difficulties – such as noise, discontinuities, expense of function evaluations, and the existence of multiple minima – that often unnecessarily inhibit the use of gradient-based methods. In a separate chapter on new gradient-based methods developed by the author and his coworkers, it is shown how these difficulties may be overcome without losing the desirable features of classical gradient-based methods.
Автор: ??nlar Название: Real and Convex Analysis ISBN: 1461452562 ISBN-13(EAN): 9781461452560 Издательство: Springer Рейтинг: Цена: 8084 р. Наличие на складе: Поставка под заказ.
Описание: The first undergraduate text to provide an accessible introduction to real and convex analysis, this book by renowned Princeton University academics covers all the fundamentals as well as the tools of analysis, and features lots of illustrations and exercises.
Описание: A survey of the methodologies that are at the confluence of several fields: Computer Science, Mathematics and Operations Research. It offers an integrated treatment of the major technologies in optimization and search methodology. It is suitable for researchers, students and practitioners across discipline domains in applied science.
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