Modified Primal Path-Following Scheme for the Monotone Variational Inequality Problem

Abstract

Recently, several interior-point methods have been developed under a scaled Lipschitz condition which may be strong in general. In this paper, we develop a modified path-following scheme which does not require the above condition. Its global convergence is proved under only the assumptions of monotonicity and differentiability of the mapping. The scheme is adapted to the network equilibrium problem (a nonlinear multicommodity network flow problem) with a simplicial decomposition technique.