| 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: |
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| 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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