Long-step strategies in interior-point primal-dual methods
Nesterov, Yu.

Date: 1997
Abstract: In this paper we analyze from a unique point of view the behavior of path-following and primal-dual potential reduction methods on nonlinear conic problems. We demonstrate that most interior-point methods with O(V~n ln(1/(Epsilon))) efficiency estimate can be considered as different strategies of minimizing a convex primal-dual potential function in an extended primal-dual space. Their efficiency estimate is a direct consequence of large local norm of the gradient of the potential function along a central path. It is shown that the neighborhood of this path is a region of the fastest decrease of the potential. Therefore the long-step path-following methods are, in a sense, the best potential-reduction strategies. We present three examples of such long-step strategies. We prove also an efficiency estimate for a pure primal-dual potential reduction method, which can be considered as an implementation of a penalty strategy based on a functional proximity measure. Using the convex primal dual potential, we prove efficiency estimates for Karmarkar-type and Dikin-type methods as applied to a homogeneous reformulation of the initial primal-dual problem.
Rights: Tots els drets reservats.
Language: Anglès
Document: Article ; recerca ; Versió publicada
Subject: Nonlinear programming ; Conic problem ; Interior-point methods ; Self-concordant barrier ; Path-following methods ; Potential-reduction methods
Published in: Mathematical Programming, vol. 76 n. 1 (1997) p. 47-94, ISSN 0025-5610



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 Record created 2006-03-13, last modified 2023-06-03



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