Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework

@article{Fukuda2001ExploitingSI,
  title={Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework},
  author={Mituhiro Fukuda and Masakazu Kojima and Kazuo Murota and Kazuhide Nakata},
  journal={SIAM Journal on Optimization},
  year={2001},
  volume={11},
  pages={647-674}
}
A critical disadvantage of primal-dual interior-point methods compared to dual interior-point methods for large scale semidefinite programs (SDPs) has been that the primal positive semidefinite matrix variable becomes fully dense in general even when all data matrices are sparse. Based on some fundamental results about positive semidefinite matrix completion, this article proposes a general method of exploiting the aggregate sparsity pattern over all data matrices to overcome this disadvantage… CONTINUE READING
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\ Exploiting sparsity in primaldual interiorpoint methods for semide nite programming

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