A modification of the Osborne and Watson algorithm for nonlinear minimax approximation

Abstract

The algorithm for nonlinear minimax approximation published by Osborne and Watson uses a sequence of linear programming problems, each of which is formed by linearisation in the neighbourhood of the solution to the preceding problem. Instead of retracing the simplex steps from the usual initial feasible basis, we commence with the final basis from the previous step. Difficulties caused by infeasibilities are discussed and numerical comparison are presented.