Two Logarithmic Barrier Methods for Convex Semi-Infinite Problems

In the first part of the paper a logarithmic barrier method for solving convex semi-infinite programming problems with bounded solution set is considered. For that the solution of a non-differentiable optimization problem by means of a logarithmic barrier method is suggested. The arising auxiliary problems are solved, for instance, via a bundle method. In the second part of the paper a regularized logarithmic barrier method for solving convex semi-infinite problems with unbounded solution set is considered, which is based on the method from the first part. The properties and the behaviour of the presented methods are studied and numerical results are given.

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