A regularized penalty method for solving convex semi-infinite programs

This paper is concerned with the stable solution of ill-posed convex semi-infinite problems on the base of their sequential approximation by finite dimensional convex problems on a sequence of grids. These auxiliary programs are constructed by using the iterative Prox-regularization and for solving each of them only one step of a penalty method is applied. A simple deletion procedure of inactive constraints is suggested. The choice of the control parameters secures the convergence of the methods and a linear convergence rate is obtained.