• Corpus ID: 16720847

A New Primal-Dual Interior-Point Method for Semidefinite Programming

@inproceedings{Alizadeh1994ANP,
  title={A New Primal-Dual Interior-Point Method for Semidefinite Programming},
  author={Farid Alizadeh and Jean Pierre Haeberly and Michael L. Overton},
  year={1994}
}
The semidefinite programming problem (SDP) is: min tr CX s.t. tr A{sub i}X = b{sub i}, i = 1, {hor_ellipsis}, m, and X {>=} 0. Here C and A{sub i} are fixed symmetric matrices and X {>=} 0 is a semidefinite constraint on the unknown symmetric matrix variable X. The dual of SDP is: max b{sup T} y s.t. Z + {Sigma}{sub i=1}{sup m} y{sub i}A{sub i} = C and Z {>=} 0. Interior point methods for SDP have been developed by Nesterov and Nemirovskii, Alizadeh, Vandenberghe and Boyd, and others. Primal… 
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59 Citations
Highly Influential Citations
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Background Citations
18
Methods Citations
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59 Citations

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References

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It is argued that many known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity carrying over in a similar fashion.
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TLDR
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