A Review of Numerical Methods for Semi-Infinite Optimization

The aim of this paper is to sketch briefly the main ideas that are fundamental in the different types of methods for solving semi-infinite problems and to discuss several difficulties that are inherent in some of them. At the same time, this gives the possibility to compare several methods and to decide in which situation they profitably can be applied. It appears that a partition of the methods in two classes is appropriate: On the one side methods suitable to improve a “good” approximation to the solution efficiently and, on the other side, those being appropriate to compute those good approximations to the solution. This suggests two phase-methods for solving semi-infinite problems. A number of examples are given to illustrate the complexity of the problems and the performance and efficiency of the methods.

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