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

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

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Article ID: iaor20041231
Country: Germany
Volume: 95
Issue: 2
Start Page Number: 329
End Page Number: 357
Publication Date: Jan 2003
Journal: Mathematical Programming
Authors: ,
Keywords: semidefinite programming
Abstract:

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.

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