Solving a class of matrix minimization problems by linear variational inequality approaches

Min Tao; Xiao Ming Yuan; Bing Sheng He

doi:10.1016/j.laa.2010.11.041

Solving a class of matrix minimization problems by linear variational inequality approaches

Min Tao, Xiao Ming Yuan, Bing Sheng He^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

4 Citations (Scopus)

Abstract

A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising.

Original language	English
Pages (from-to)	2343-2352
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	11
DOIs	https://doi.org/10.1016/j.laa.2010.11.041
Publication status	Published - 1 Jun 2011

Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

User-Defined Keywords

Matrix minimization
Projection and contraction method

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10.1016/j.laa.2010.11.041

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title = "Solving a class of matrix minimization problems by linear variational inequality approaches",

abstract = "A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising.",

keywords = "Matrix minimization, Projection and contraction method",

author = "Min Tao and Yuan, {Xiao Ming} and He, {Bing Sheng}",

note = "Funding Information: Corresponding author. E-mail addresses: [email protected] (X.-m. Yuan), [email protected] (B.-s. He). 1 This author was supported by the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY210049). 2 This author was supported by the RGC 203009, Hong Kong. 3 This author was supported by the NSFC Grant 10971095 and Jiangsu NSF BK2008255.",

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doi = "10.1016/j.laa.2010.11.041",

language = "English",

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T1 - Solving a class of matrix minimization problems by linear variational inequality approaches

AU - Tao, Min

AU - Yuan, Xiao Ming

AU - He, Bing Sheng

N1 - Funding Information: Corresponding author. E-mail addresses: [email protected] (X.-m. Yuan), [email protected] (B.-s. He). 1 This author was supported by the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY210049). 2 This author was supported by the RGC 203009, Hong Kong. 3 This author was supported by the NSFC Grant 10971095 and Jiangsu NSF BK2008255.

PY - 2011/6/1

Y1 - 2011/6/1

N2 - A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising.

AB - A class of matrix optimization problems can be formulated as a linear variational inequalities with special structures. For solving such problems, the projection and contraction method (PC method) is extended to variational inequalities with matrix variables. Then the main costly computational load in PC method is to make a projection onto the semi-definite cone. Exploiting the special structures of the relevant variational inequalities, the Levenberg-Marquardt type projection and contraction method is advantageous. Preliminary numerical tests up to 1000×1000 matrices indicate that the suggested approach is promising.

KW - Matrix minimization

KW - Projection and contraction method

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U2 - 10.1016/j.laa.2010.11.041

DO - 10.1016/j.laa.2010.11.041

M3 - Journal article

AN - SCOPUS:79952624785

SN - 0024-3795

VL - 434

SP - 2343

EP - 2352

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 11

ER -

Solving a class of matrix minimization problems by linear variational inequality approaches

Abstract

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