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" First-order methods in optimization / "
Amir Beck, Technion-Israel Institute for Technology, Technion, Haifa, Israel.
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BL
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| Record Number
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854438
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| Main Entry
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Beck, Amir
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| Title & Author
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First-order methods in optimization /\ Amir Beck, Technion-Israel Institute for Technology, Technion, Haifa, Israel.
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| Publication Statement
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Philadelphia, Pennsylvania :: Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),, [2017]
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| Series Statement
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MOS-SIAM series on optimization ;; 25
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| Page. NO
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1 online resource (x, 484 pages).
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| ISBN
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1611974992
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: 9781611974997
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9781611974980
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Includes bibliographical references and index.
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| Contents
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Vector spaces -- Extended real-value functions -- Subgradients -- Conjugate functions -- Smoothness and strong convexity -- The proximal operator -- Spectral functions -- Primal and dual projected subgradient methods -- Mirror descent -- The proximal gradient method -- The block proximal gradient method -- Dual-based proximal gradient methods -- The generalized Conditional gradient method -- Alternating minimization -- ADMM.
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| Abstract
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The primary goal of this book is to provide a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
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| Subject
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Convergence.
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Mathematical optimization.
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Convergence.
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Mathematical optimization.
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| Dewey Classification
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519.6
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| LC Classification
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QA402.5.B42238 2017eb
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QA402.5
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| Added Entry
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Society for Industrial and Applied Mathematics,publisher.
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