Self-Scaled Barriers and Interior-Point Methods for Convex Programming

@article{Nesterov1997SelfScaledBA,
  title={Self-Scaled Barriers and Interior-Point Methods for Convex Programming},
  author={Yurii Nesterov and Michael J. Todd},
  journal={Math. Oper. Res.},
  year={1997},
  volume={22},
  pages={1-42}
}
This paper provides a theoretical foundation for efficient interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled. For such problems we devise long-step and symmetric primal-dual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit… CONTINUE READING

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