Algorithms for convex optimization /, Vishnoi, Nisheeth K.,

Автор: Stephen Boyd
Название: Convex Optimization
ISBN: 0521833787 ISBN-13(EAN): 9780521833783
Издательство: Cambridge Academ
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Цена: 119670.00 T
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Описание: The focus of this 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: Nisheeth K. Vishnoi
Название: Algorithms for Convex Optimization
ISBN: 1108482023 ISBN-13(EAN): 9781108482028
Издательство: Cambridge Academ
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Цена: 87650.00 T
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Описание: Algorithms for Convex Optimization are the workhorses of data-driven, technological advancements in machine learning and artificial intelligence. This concise, modern guide to deriving these algorithms is self-contained and accessible to advanced students, practitioners, and researchers in computer science, operations research, and data science.

Автор: Juditsky Anatoli, Nemirovski Arkadi
Название: Statistical Inference Via Convex Optimization
ISBN: 0691197296 ISBN-13(EAN): 9780691197296
Издательство: Wiley
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Цена: 92930.00 T
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Описание:

This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences.

Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems--sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals--demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems.

Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

Автор: Roman G. Strongin; Yaroslav D. Sergeyev
Название: Global Optimization with Non-Convex Constraints
ISBN: 0792364902 ISBN-13(EAN): 9780792364900
Издательство: Springer
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Цена: 287890.00 T
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Описание: Presents a new approach to global non-convex constrained optimization. Problem dimensionality is reduced via space-filling curves and to economize the search, constraint is accounted separately (penalties are not employed). The multicriteria case is also considered.

Автор: Borwein, Jonathan M. Lewis, Adrian S. (university Of Waterloo)
Название: Convex analysis and nonlinear optimization
ISBN: 1441921273 ISBN-13(EAN): 9781441921277
Издательство: Springer
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Цена: 55850.00 T
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Описание: Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This new edition adds material on semismooth optimization, as well as several new proofs.

Автор: Aram Arutyunov, Valeri Obukhovskii
Название: Convex and Set-Valued Analysis
ISBN: 3110460289 ISBN-13(EAN): 9783110460285
Издательство: Walter de Gruyter
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Цена: 74320.00 T
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Описание: This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents: PrefacePart I: Convex analysisConvex sets and their propertiesThe convex hull of a set. The interior of convex setsThe affine hull of sets. The relative interior of convex setsSeparation theorems for convex setsConvex functionsClosedness, boundedness, continuity, and Lipschitz property of convex functionsConjugate functionsSupport functionsDifferentiability of convex functions and the subdifferentialConvex conesA little more about convex cones in infinite-dimensional spacesA problem of linear programmingMore about convex sets and convex hullsPart II: Set-valued analysisIntroduction to the theory of topological and metric spacesThe Hausdorff metric and the distance between setsSome fine properties of the Hausdorff metricSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued mapsA base of topology of the spaceHc(X)Measurable set-valued maps. Measurable selections and measurable choice theoremsThe superposition set-valued operatorThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximationsSpecial selections of set-valued mapsDifferential inclusionsFixed points and coincidences of maps in metric spacesStability of coincidence points and properties of covering mapsTopological degree and fixed points of set-valued maps in Banach spacesExistence results for differential inclusions via the fixed point methodNotationBibliographyIndex

Автор: Alexander M. Rubinov; Xiao-qi Yang
Название: Lagrange-type Functions in Constrained Non-Convex Optimization
ISBN: 1461348218 ISBN-13(EAN): 9781461348214
Издательство: Springer
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Цена: 93160.00 T
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Описание: Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza- tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints.

Автор: Roman G. Strongin; Yaroslav D. Sergeyev
Название: Global Optimization with Non-Convex Constraints
ISBN: 1461371171 ISBN-13(EAN): 9781461371175
Издательство: Springer
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Цена: 139750.00 T
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Автор: Nesterov
Название: Lectures on Convex Optimization
ISBN: 3319915770 ISBN-13(EAN): 9783319915777
Издательство: Springer
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Цена: 55890.00 T
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Описание: The first elementary exposition of core ideas of complexity theory for convex optimization, this book explores optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. Also covers polynomial-time interior-point methods.

Автор: Miroslav Bacak
Название: Convex analysis and optimization in Hadamard spaces
ISBN: 3110361035 ISBN-13(EAN): 9783110361032
Издательство: Walter de Gruyter
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Цена: 136310.00 T
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Описание: In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.

Автор: Panos M. Pardalos; Antanas ?ilinskas; Julius ?ilin
Название: Non-Convex Multi-Objective Optimization
ISBN: 3319610058 ISBN-13(EAN): 9783319610054
Издательство: Springer
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Цена: 83850.00 T
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Описание: Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions.

Название: Selected Applications of Convex Optimization
ISBN: 3662463555 ISBN-13(EAN): 9783662463550
Издательство: Springer
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Цена: 46570.00 T
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Описание: This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems.