A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization

In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according...

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Bibliographic Details
Published in:Mathematical programming Vol. 95; no. 2; pp. 329 - 357
Main Authors: Burer, Samuel, Monteiro, Renato D.C.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.02.2003
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Digital Object Identifier
Exact sciences and technology
Mathematical programming
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Optimization techniques
Semidefinite programming
Sparsity
Variables
semidefinite programming
Lagrangian
nonlinear programming
Semi definite programming
limited memory BFGS
Matrix factorization
Non linear programming
augmented Lagrangian
low-rank factorization
Mathematical programming
Large scale system
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X=RRT. The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems are also presented.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-002-0352-8