An interior-point method for semi-infinite programming problems

This work examines the generalization of a certain interior-point method, namely the method of analytic centers, to semi-infinite linear programming problems. The paper defines an analytic center for these problems and an appropriate norm to examine Newton’s method for computing this center. A simple algorithm of order zero is constructed and a convergence proof for that algorithm is given. Finally, the paper describes a more practical implementation of a predictor-corrector method and give some numerical results. In particular it concentrates on practical integration rules that take care of the specific structure of the integrals.