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|a Parikh, Neal,
|e author
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|a Proximal algorithms /
|c Neal Parikh, Stephen Boyd
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|a [Hanover, Massachusetts] :
|b Now Publishers,
|c 2014
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|a 1 online resource (1 PDF (iii, 128-239 pages))
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|a Foundations and trends in optimization,
|x 2167-3918 ;
|v volume 1, issue 3, pages 127-239
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|a Title from PDF (viewed on December 04, 2014)
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|a Includes bibliographical references (pages 224-239)
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|a 1. Introduction -- 1.1 Definition -- 1.2 Interpretations -- 1.3 Proximal algorithms -- 1.4 What this paper is about -- 1.5 Related work -- 1.6 Outline
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8 |
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|a 2. Properties -- 2.1 Separable sum -- 2.2 Basic operations -- 2.3 Fixed points -- 2.4 Proximal average -- 2.5 Moreau decomposition
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|a 3. Interpretations -- 3.1 Moreau-Yosida regularization -- 3.2 Resolvent of subdifferential operator -- 3.3 Modified gradient step -- 3.4 Trust region problem -- 3.5 Notes and references
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| 505 |
8 |
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|a 4. Proximal algorithms -- 4.1 Proximal minimization -- 4.2 Proximal gradient method -- 4.3 Accelerated proximal gradient method -- 4.4 Alternating direction method of multipliers -- 4.5 Notes and references
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| 505 |
8 |
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|a 5. Parallel and distributed algorithms -- 5.1 Problem structure -- 5.2 Consensus -- 5.3 Exchange -- 5.4 Allocation -- 5.5 Notes and references
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| 505 |
8 |
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|a 6. Evaluating proximal operators -- 6.1 Generic methods -- 6.2 Polyhedra -- 6.3 Cones -- 6.4 Pointwise maximum and supremum -- 6.5 Norms and norm balls -- 6.6 Sublevel set and epigraph -- 6.7 Matrix functions -- 6.8 Notes and references
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| 505 |
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|a 7. Examples and applications -- 7.1 Lasso -- 7.2 Matrix decomposition -- 7.3 Multi-period portfolio optimization -- 7.4 Stochastic optimization -- 7.5 Robust and risk-averse optimization -- 7.6 Stochastic control
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|a 8. Conclusions -- References
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| 510 |
0 |
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|a ACM Computing Guide
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| 510 |
0 |
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|a ACM Computing Reviews
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| 510 |
0 |
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|a AMS MathSciNet
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| 510 |
0 |
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|a DBLP Computer Science Bibliography
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| 510 |
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|a Google Book Search
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| 510 |
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|a Google Scholar
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| 510 |
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|a INSPEC
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| 510 |
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|a Scopus
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|a Zentralblatt MATH Database
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|a This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Here, we discuss the many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some popular algorithms, and provide a large number of examples of proximal operators that commonly arise in practice
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| 524 |
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|a Foundations and Trends in Optimization, Vol. 1, No. 3 (2014) 127-239, 2014, N. Parikh and S. Boyd
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|a Algorithms
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|a Mathematical optimization
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|a Algorithms
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|a Mathematical optimization
|2 fast
|0 http://id.worldcat.org/fast/1012099
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|a Boyd, Stephen P
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