The semismooth approach for semi-infinite programming under the Reduction Ansatz |
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Authors: | Oliver Stein Aysun Tezel |
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Institution: | (1) School of Economics and Business Engineering, University of Karlsruhe, Karlsruhe, Germany;(2) Department of Mathematics, Middle East Technical University, Ankara, Turkey |
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Abstract: | We study convergence of a semismooth Newton method for generalized semi-infinite programming problems with convex lower level
problems where, using NCP functions, the upper and lower level Karush-Kuhn-Tucker conditions of the optimization problem are
reformulated as a semismooth system of equations. Nonsmoothness is caused by a possible violation of strict complementarity
slackness. We show that the standard regularity condition for convergence of the semismooth Newton method is satisfied under
natural assumptions for semi-infinite programs. In fact, under the Reduction Ansatz in the lower level and strong stability
in the reduced upper level problem this regularity condition is satisfied. In particular, we do not have to assume strict
complementary slackness in the upper level. Numerical examples from, among others, design centering and robust optimization
illustrate the performance of the method.
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Keywords: | Generalized semi-infinite optimization Semismooth Newton method NCP function CD-regularity Reduction Ansatz |
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