Proximal Algorithms Neal Parikh

ISBN: 9781601987167

Published: November 27th 2013

Paperback

128 pages


Description

Proximal Algorithms  by  Neal Parikh

Proximal Algorithms by Neal Parikh
November 27th 2013 | Paperback | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 128 pages | ISBN: 9781601987167 | 6.26 Mb

Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newtons methodMoreProximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular.

Much like Newtons 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 Newtons 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. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.



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