Proximal Interior Point Approach for Solving Convex Semi-infinite Programming Problems

1 A regularized logarithmic barrier method for solving ill-posed convex semi-infinite programming problems is considered. In this method a multistep proximal regularization is coupled with an adaptive discretization strategy in the framework of the 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 suggested is studied as well as conditions, ensuring linear convergence for both the objective values and the iterates. Stability of the method is proved with respect to data perturbations in the cone of convex C-functions.