Solving semi-infinite optimization problems with interior point techniques

Oliver Stein and Georg Still

Abstract. We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method bases upon a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized NCP functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smooth non-linear finite optimization problem has to be solved. The solution of the semi-infinite optimization problem then amounts to driving the path parameter to zero.

We show convergence properties of the algorithm and give a number of numerical examples, including problems from design centering and from robust optimization, where actually so-called generalized semi-infinite optimization problems are solved. The presented algorithm is easy to implement, and our examples show that it works well for dimensions of the semi-infinite index set at least up to 150.

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