# Primal-Dual Affine-Scaling Algorithms Fail for Semidefinite Programming

@article{Muramatsu1999PrimalDualAA,
title={Primal-Dual Affine-Scaling Algorithms Fail for Semidefinite Programming},
author={Masakazu Muramatsu and Robert J. Vanderbei},
journal={Math. Oper. Res.},
year={1999},
volume={24},
pages={149-175}
}
• Published 1 February 1999
• Mathematics
• Math. Oper. Res.
In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithms can generate a sequence converging to a non-optimal solution and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with these directions, we show that the primal-dual affine-scaling algorithm using the NT direction for…

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