The charges on the paths

Nonlinear complementarity problems NCP(F) have many practical applications. For NCPs arising from traffic equilibrium, the mapping F usually does not have explicit forms and only its value can be evaluated/observed for given variables. In this paper, such problems are called implicit NCPs. We concern the devised methods which only use the observed function values in the solution process. The goals of this paper are twofold: first, we point out that the mathematical form of some essential applications in traffic is an implicit NCP, and second, an effective direct method for solving monotone implicit NCPs is introduced.