The convergence conditions of diagonalization and projection methods for fixed demand asymmetric network equilibrium problems

We have considered algorithms proposed for solving the fixed demand user optimized network equilibrium problems with asymmetric user costs. Making use of the property that the problem can be expressed in the form of a variational inequality, there are many methods which are proposed in the literature. For example, the projection methods and the diagonalization method are developed. But the convergence of these variational inequality methods often requires restrictive conditions. We have assessed the relevance of these conditions with respect to the asymmetry level of the cost function.