Distributed convex optimization with proximal methods
Abstract/Contents
- Abstract
- This thesis 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, distributed, or decentralized 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 \emph{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 many different interpretations of proximal operators and algorithms, describe their connections to many other topics in optimization and applied mathematics, survey some fundamental algorithms, and provide a large number of examples of proximal operators that arise in practice.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2014 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Parikh, Neal |
|---|---|
| Associated with | Stanford University, Department of Computer Science. |
| Primary advisor | Boyd, Stephen P |
| Thesis advisor | Boyd, Stephen P |
| Thesis advisor | Koller, Daphne |
| Thesis advisor | Liang, Percy |
| Advisor | Koller, Daphne |
| Advisor | Liang, Percy |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Neal Parikh. |
|---|---|
| Note | Submitted to the Department of Computer Science. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2014. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2014 by Neal Parikh
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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