Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

@article{Alizadeh1998PrimalDualIM,
  title={Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results},
  author={Farid Alizadeh and Jean Pierre Haeberly and Michael L. Overton},
  journal={SIAM J. Optim.},
  year={1998},
  volume={8},
  pages={746-768}
}
Primal-dual interior-point path-following methods for semidefinite programming are considered. Several variants are discussed, based on Newton's method applied to three equations: primal feasibility, dual feasibility, and some form of centering condition. The focus is on three such algorithms, called the XZ, XZ+ZX, and Q methods. For the XZ+ZX and Q algorithms, the Newton system is well defined and its Jacobian is nonsingular at the solution, under nondegeneracy assumptions. The associated… 

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