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

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...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications Vol. 32; no. 1; pp. 136 - 152
Main Authors: He, Bingsheng, Xu, Minghua, Yuan, Xiaoming
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Algebra
Calculus of variations and optimal control
Exact sciences and technology
Global analysis, analysis on manifolds
Intersections
Least squares method
Linear and multilinear algebra, matrix theory
Linear equations
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Matrices
Matrix
Matrix methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Programming
Sciences and techniques of general use
Semidefinite programming
Studies
Tasks
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Intersection
Alternating direction method
Cone
Solving
Least squares problem
Square matrix
Optimization method
90C06
Semi definite programming
least squares semidefinite matrix
Constrained optimization
Linear constraint
Numerical analysis
Efficiency
Variational inequality
Symmetric matrix
Least squares method
90C25
90C22
Linear algebra
49M29
Large scale
large-scale
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Summary: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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ISSN:0895-4798
1095-7162
DOI:10.1137/090768813