Discretization in semi-infinite programming: the rate of convergence

The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the convergence rate of the error betw een the solution of the semi-infinite problem and the solution of the discr etized program depending on the discretization mesh-size. It will be shown how this rate depends on whether the minimizer is strict of order one or tw o and on whether the discretization includes boundary points of the index s et in aspecific way. This is done for ordinary and for generalized semi-inf inite problems.