The semismooth approach for semi-infinite programming under the reduction ansatz (Q933800)

A semismooth Newton method for solving generalized semi-infinite programming problems (GSIP) is proposed and analyzed. The method is based on the KKT system where the complementarity conditions are replaced by a formulation using NCP functions. The approach is studied for GSIP with convex lower level problems. It is shown that under standard assumptions at a local minimizer of GSIP (reduction ansatz and strict complementarity in the lower level, linear independency constraint qualification and strong second order sufficiency condition in the upper level) the standard assumptions for convergence of the semismooth Newton system holds such that the method converges q-quadratically. The approach does not assume strict comlementarity in the upper level, so that the standard KKT Newton system is singular. The paper also presents some interesting numerical examples.