A Subgradient Projection Method for Set-Valued Network Equilibrium Problems

Abstract

In the present work, we describe a general set-valued variant of the network equilibrium problem with fixed demand. This problem is equivalent to a set-valued variational inequality. Under certain additional assumptions, it can be replaced with a nonsmooth convex optimization problem. We propose to apply the subgradient projection method with a special two-speed step-size choice procedure to this problem. Computational experiments on model networks showed that the proposed approach is rather efficient. It gives a more flexible procedure for the choice of parameters.