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A Nonlinear Programming Algorithm for Solving Semidefinite Programs via Low-rank Factorization

Samuel Burer (burer***at***math.gatech.edu)
Renato D.C. Monteiro (monteiro***at***isye.gatech.edu)

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 = RR^T. 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.

Keywords: semidefinite programming, low-rank factorization, nonlinear programming

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: School of ISyE Georgia Tech Atlanta, GA 30332 March 2001

Download: [Postscript][PDF]

Entry Submitted: 03/09/2001
Entry Accepted: 03/10/2001
Entry Last Modified: 03/22/2001

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