A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Burer, S. & Monteiro, R. D. 95(2):329–357.
Paper doi abstract bibtex 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.
@article{burer-monterio-mp03,
title = {A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization},
volume = {95},
issn = {1436-4646},
url = {https://doi.org/10.1007/s10107-002-0352-8},
doi = {10.1007/s10107-002-0352-8},
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.},
pages = {329--357},
number = {2},
journaltitle = {Mathematical Programming},
shortjournal = {Math. Program., Ser. B},
author = {Burer, Samuel and Monteiro, Renato D.C.},
urldate = {2024-08-26},
date = {2003-02-01},
langid = {english},
keywords = {Computational Result, Nonlinear Programming, Programming Algorithm, Standard Form, Test Problem},
file = {Full Text PDF:/Users/ukreddy/Zotero/storage/RCMEBBLK/Burer and Monteiro - 2003 - A nonlinear programming algorithm for solving semi.pdf:application/pdf},
}
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