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First-Order Methods for Trace Norm M...

Chao, Hsiao-Han.

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First-Order Methods for Trace Norm Minimization.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	First-Order Methods for Trace Norm Minimization./
Author:	Chao, Hsiao-Han.
Description:	67 p.
Notes:	Source: Masters Abstracts International, Volume: 51-06.
Contained By:	Masters Abstracts International51-06(E).
Subject:	Engineering, Electronics and Electrical. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1538945
ISBN:	9781303132759

First-Order Methods for Trace Norm Minimization.
Chao, Hsiao-Han.

First-Order Methods for Trace Norm Minimization. - 67 p.

Source: Masters Abstracts International, Volume: 51-06.

Thesis (M.S.)--University of California, Los Angeles, 2013.

Minimizing the trace norm (sum of singular values) of a matrix has become popular as a convex heuristic for computing low rank approximations, with numerous applications in control, system theory, statistics, and machine learning. However, it is usually too expensive to solve these matrix optimization problems with second-order methods, such as the interior-point method, given that the scale of the problems is relatively large. In this thesis, we compare several first-order methods for nondifferentiable convex optimization based on splitting algorithms, and apply them to primal, dual, or primal-dual optimality conditions. The implementation aspects of the algorithms are discussed in detail and their performance is compared in experiments with randomly generated data as well as system identification test sets. We show that on large-scale problems, several of the first-order methods reach a modest accuracy within a shorter time than the interior-point solvers. Based on the experiments, the most promising methods are the Alternating Direction Method of Multipliers and the Pock-Chambolle semi-implicit algorithm.

ISBN: 9781303132759Subjects--Topical Terms:

626636
Engineering, Electronics and Electrical.

First-Order Methods for Trace Norm Minimization.
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100 1 $a Chao, Hsiao-Han. $3 2092080
245 1 0 $a First-Order Methods for Trace Norm Minimization.
300 $a 67 p.
500 $a Source: Masters Abstracts International, Volume: 51-06.
500 $a Adviser: Lieven Vandenberghe.
502 $a Thesis (M.S.)--University of California, Los Angeles, 2013.
520 $a Minimizing the trace norm (sum of singular values) of a matrix has become popular as a convex heuristic for computing low rank approximations, with numerous applications in control, system theory, statistics, and machine learning. However, it is usually too expensive to solve these matrix optimization problems with second-order methods, such as the interior-point method, given that the scale of the problems is relatively large. In this thesis, we compare several first-order methods for nondifferentiable convex optimization based on splitting algorithms, and apply them to primal, dual, or primal-dual optimality conditions. The implementation aspects of the algorithms are discussed in detail and their performance is compared in experiments with randomly generated data as well as system identification test sets. We show that on large-scale problems, several of the first-order methods reach a modest accuracy within a shorter time than the interior-point solvers. Based on the experiments, the most promising methods are the Alternating Direction Method of Multipliers and the Pock-Chambolle semi-implicit algorithm.
590 $a School code: 0031.
650 4 $a Engineering, Electronics and Electrical. $3 626636
650 4 $a Applied Mathematics. $3 1669109
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710 2 $a University of California, Los Angeles. $b Electrical Engineering 0303. $3 2092079
773 0 $t Masters Abstracts International $g 51-06(E).
790 $a 0031
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792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1538945