MULTIPOINT METHODS FOR SEPARABLE NONLINEAR NETWORKS.

Iterative piecewise-linear approximation methods are considered for separable, convex nonlinear network problems. A comparison is made between 'fixed grid' approximations of 2, 4, and 6 segments per variable and 'implicit grid' strategies that generate segments as needed, but store at most a 2-segment approximation at any time. It is shown that the implicit grid methods are linearly convergent, and this predicted behavior is confirmed by highly accurate solutions within 7 iterations of problems with up to 2238 variables. Since the computing time per iteration is only slightly more for implicit grids than for fixed grids, the numerical results presented show overall computing times are less for implicit grids. A lower bounding technique based on the error of approximation is also developed.