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

@article{Burer2003ANP, title={A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization}, author={Samuel Burer and Renato D. C. Monteiro}, journal={Mathematical Programming}, year={2003}, volume={95}, pages={329-357} }

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…

## 747 Citations

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