Discretization methods for the solution of semi-infinite programming problems

In the first part of this paper, the convergence of a class of discretization methods is proven for the solution of nonlinear semiinfinite programming problems, which includes known methods for linear problems as special cases. In the second part, this type of algorithms is modified for linear problems and a specific method is given which requires the solution of a quadratic programming problem at each iteration. With this algorithm, satisfactory results can also be obtained for a number of singular problems. The performance of the algorithm is illustrated with several numerical examples of multivariate Chebyshev approximation problems. (Author)