Discretization methods for the solution of semi-infinite programming problems

Abstract

In the first part of this paper, we prove the convergence of a class of discretization methods for the solution of nonlinear semi-infinite programming problems, which includes known methods for linear problems as special cases. In the second part, we modify and study this type of algorithms for linear problems and suggest a specific method 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. We demonstrate the performance of the algorithm by several numerical examples of multivariate Chebyshev approximation problems.