Proximal interior point method for convex semi-infinite programming
Alexander Kaplan, Rainer Tichatschke · Optimization methods & software · 2001
A regularized logarithmic Barrier method for solving (ill-posed) convex semi-infinite programming problems is considered. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. Termination of the proximal iterations at each discretization level is controlled by means of estimates, characterizing the efficiency of these iterations. A special deleting rule permits to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convex C 1-functions are studied as well as some numerical experiments are presented.