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Zbl 0871.90064
Nesterov, Yu.E.; Todd, M.J.
Self-scaled barriers and interior-point methods for convex programming. (English)
[J] Math. Oper. Res. 22, No.1, 1-42 (1997). ISSN 1526-5471; ISSN 0364-765X/e

Summary: 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 radius in the local norm defined by the Hessian of the barrier.

MSC 2000:: *90C25 Convex programming
90C05 Linear programming
65Y20 Complexity and performance of numerical algorithms

Keywords: self-scaled cone; self-scaled barrier; path-following; potential-reduction algorithms; interior-point algorithms

Cited in: Zbl 1220.90082 Zbl 1027.90066 Zbl 0957.90104 Zbl 0956.90026 Zbl 0922.90110 Zbl 0913.65051

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