Self-Scaled Cones and Interior-Point Methods in Nonlinear Programming

Yurii E. Nesterov . () and Michael Todd
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Yurii E. Nesterov .: CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium

No 1994062, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: This paper provides a theoretical foundation for efficient interior-point algorithms for nonlinear 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.

Keywords: Nonlinear programming; conical form; interior point algorithms; selfconcordant barrier; self-scaled cone; self-scaled barrier; path-following algorithms; potential-reduction algorithms (search for similar items in EconPapers)
Date: 1994-11-01
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:1994062

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