PATH-FOLLOWING PROXIMAL APPROACH FOR SOLVING ILL-POSED CONVEX SEMIINFINITE PROGRAMMING-PROBLEMS

For a class of ill-posed, convex semi-infinite programming problems, a regularized path-following strategy is developed. This approach consi sts in a coordinated application of adaptive discretization and prox-r egularization procedures combined with a penalty method. At each itera tion, only an approximate minimum of a strongly convex differentiable function has to be calculated, and this can be done by any fast-conver gent algorithm. The use of prox-regularization ensures the convergence of the iterates to some solution of the original problem. Due to regu larization, an efficient deleting rule is applicable, which excludes a n essential part of the constraints in the discretized problems.