The semismooth approach for semi-infinite programming without strict complementarity

Abstract. As a complement of our recent article O. Stein, A. Tezel, The semismooth approach for semi-infinite programming under the Reduction Ansatz, 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 NCP functions into a semismooth system of equations.

In the present paper we neither assume strict complementary slackness in the upper nor in the lower level. The auxiliary functions of the locally reduced problem are then not necessarily twice differentiable. Still, we can show that a standard regularity condition for quadratic convergence of the semi-smooth Newton method holds under a natural assumption for semi-infinite programs.