A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization |
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Authors: | Samuel Burer Renato DC Monteiro |
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Institution: | (1) Department of Management Sciences, University of Iowa, Iowa City, IA 52242-1000, e-mail: burer@math.gatech.edu, US;(2) School of ISyE, Georgia Tech, Atlanta, GA 30332, USA,e-mail:monteiro@isye.gate, US |
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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.
Received: March 22, 2001 / Accepted: August 30, 2002 Published online: December 9, 2002
Key Words. semidefinite programming – low-rank factorization – nonlinear programming – augmented Lagrangian – limited memory BFGS
This research was supported in part by the National Science Foundation under grants CCR-9902010, INT-9910084, CCR-0203426
and CCR-0203113 |
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