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

Data: 1997
Resum: 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. .
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Nonlinear programming ; Conic problem ; Interior-point methods ; Self-concordant barrier ; Path-following methods ; Potential-reduction methods
Publicat a: Mathematical Programming, vol. 76 n. 1 (1997) p. 47-94, ISSN 0025-5610

48 p, 1.8 MB
 Accés restringit a la UAB

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