# Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

@article{Alizadeh1995InteriorPM, title={Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization}, author={Farid Alizadeh}, journal={SIAM J. Optim.}, year={1995}, volume={5}, pages={13-51} }

This paper studies the semidefinite programming SDP problem, i.e., the optimization problem of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First the classical cone duality is reviewed as it is specialized to SDP is reviewed. Next an interior point algorithm is presented that converges to the optimal solution in polynomial time. The approach is a direct extension of Ye’s projective method…

## 987 Citations

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