The semismooth approach for semi-infinite programming under the Reduction Ansatz

Authors:
Oliver Stein;Aysun Tezel
Affiliations:
School of Economics and Business Engineering, University of Karlsruhe, Karlsruhe, Germany;Department of Mathematics, Middle East Technical University, Ankara, Turkey
Venue:
Journal of Global Optimization
Year:
2008

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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.