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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| Vydané v: | SIAM journal on matrix analysis and applications Ročník 32; číslo 1; s. 136 - 152 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Philadelphia, PA
Society for Industrial and Applied Mathematics
01.01.2011
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| ISSN: | 0895-4798, 1095-7162 |
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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. |
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| AbstractList | 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. [PUBLICATION 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. |
| Author | Yuan, Xiaoming Xu, Minghua He, Bingsheng |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods |
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