AFFINE-SCALING TRAJECTORIES ASSOCIATED WITH A SEMIINFINITE LINEAR PROGRAM

Semi-infinite linear programs often arise as the limit of a sequence o f approximating linear programs. Hence, studying the behavior of exten sions of linear programming algorithms to semi-infinite problems can y ield valuable insight into the behavior of the underlying linear progr amming algorithm when the number of constraints or the number of varia bles is very large. In this paper, we study the behavior of the affine -scaling algorithm on a particular semi-infinite linear programming pr oblem. We show that the continuous trajectories converge to the optima l solution but that, for any strictly positive step, there are startin g points for which the discrete algorithm converges to nonoptimal boun dary points.