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… 
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