Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods

Bingsheng He; Minghua Xu; Xiaoming Yuan

doi:10.1137/090768813

Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods

Bingsheng He, Minghua Xu, Xiaoming Yuan^*

^*Corresponding author for this work

Department of Mathematics

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

83 Citations (Scopus)

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Abstract

The well-known least squares semidefinite programming (LSSDP) problem seeks the nearest adjustment of a given symmetric matrix in the intersection of the cone of positive semidefinite matrices and a set of linear constraints, and it captures many applications in diversing fields. The task of solving large-scale LSSDP with many linear constraints, however, is numerically challenging. This paper mainly shows the applicability of the classical alternating direction method (ADM) for solving LSSDP and convinces the efficiency of the ADM approach. We compare the ADM approach with some other existing approaches numerically, and we show the superiority of ADM for solving large-scale LSSDP.

Original language	English
Pages (from-to)	136-152
Number of pages	17
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	32
Issue number	1
DOIs	https://doi.org/10.1137/090768813
Publication status	Published - 8 Feb 2011

Scopus Subject Areas

Analysis

User-Defined Keywords

Alternating direction method
Large-scale
Least squares semidefinite matrix
Variational inequality

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title = "Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods",

abstract = "The well-known least squares semidefinite programming (LSSDP) problem seeks the nearest adjustment of a given symmetric matrix in the intersection of the cone of positive semidefinite matrices and a set of linear constraints, and it captures many applications in diversing fields. The task of solving large-scale LSSDP with many linear constraints, however, is numerically challenging. This paper mainly shows the applicability of the classical alternating direction method (ADM) for solving LSSDP and convinces the efficiency of the ADM approach. We compare the ADM approach with some other existing approaches numerically, and we show the superiority of ADM for solving large-scale LSSDP.",

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N2 - The well-known least squares semidefinite programming (LSSDP) problem seeks the nearest adjustment of a given symmetric matrix in the intersection of the cone of positive semidefinite matrices and a set of linear constraints, and it captures many applications in diversing fields. The task of solving large-scale LSSDP with many linear constraints, however, is numerically challenging. This paper mainly shows the applicability of the classical alternating direction method (ADM) for solving LSSDP and convinces the efficiency of the ADM approach. We compare the ADM approach with some other existing approaches numerically, and we show the superiority of ADM for solving large-scale LSSDP.

AB - The well-known least squares semidefinite programming (LSSDP) problem seeks the nearest adjustment of a given symmetric matrix in the intersection of the cone of positive semidefinite matrices and a set of linear constraints, and it captures many applications in diversing fields. The task of solving large-scale LSSDP with many linear constraints, however, is numerically challenging. This paper mainly shows the applicability of the classical alternating direction method (ADM) for solving LSSDP and convinces the efficiency of the ADM approach. We compare the ADM approach with some other existing approaches numerically, and we show the superiority of ADM for solving large-scale LSSDP.

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Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods

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