SOME OUTER APPROXIMATION METHODS FOR SEMIINFINITE OPTIMIZATION PROBLEMS

The paper starts with a simple model and convergence theorem for outer approximation methods. This general framework is used to unifyingly derive and modify certain exchange methods, cutting methods and discretization methods for semi-infinite programming problems. By that, in particular, a cutting plane method for convex semi-infinite programs is developed. For a practically reasonable specification (the method is more generally stated), the subproblems in the given algorithm are moderately sized quadratic problems, and each step of the algorithm can be performed by means of finitely many operations.