THE SEMISMOOTH APPROACH FOR SEMI-INFINITE PROGRAMMING WITHOUT STRICT COMPLEMENTARITY

Date

2009-01-01

Author

Stein, Oliver
Tezel, Aysun

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As a complement of our recent article [O. Stein and A. Tezel, J. Global Optim., 41 (2008), pp. 245-266], we study convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level problems. The semismooth Newton method is applied to a semismooth reformulation of the upper and lower level Karush-Kuhn-Tucker conditions by nonlinear complementarity problem functions into a semismooth system of equations. In the present paper we assume strict complementary slackness neither in the upper nor in the lower level. The auxiliary functions of the locally reduced problem then are not necessarily twice continuously differentiable. Still, we can show that a standard regularity condition for quadratic convergence of the semismooth Newton method holds under a natural assumption for semi-infinite programs.

Subject Keywords

Theoretical Computer Science, Software

URI

https://hdl.handle.net/11511/64524

Journal

SIAM JOURNAL ON OPTIMIZATION

DOI

https://doi.org/10.1137/080719765

Collections

Department of Physics, Article

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Citation Formats

O. Stein and A. Tezel, “THE SEMISMOOTH APPROACH FOR SEMI-INFINITE PROGRAMMING WITHOUT STRICT COMPLEMENTARITY,” SIAM JOURNAL ON OPTIMIZATION, pp. 1052–1072, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64524.