A modulus-based matrix splitting method for the vertical nonlinear complementarity problem

Many applications arising in control theory, nonlinear networks, generalized Leontief input–output model and economics lead to a broad range of optimization and equilibrium problems. Under suitable convexity assumptions, the equilibrium conditions of such problems may be compactly stated as the vertical nonlinear complementarity problem (VNCP). In this paper, based on modulus-based formulation of the VNCP, we present a variety of modulus-based matrix splitting methods for solving the VNCP. Under some mild conditions, we establish the convergence of the proposed method. Numerical experiments indicate that the proposed method is effective.