A high-performance nonlinear dynamic scheme for the solution of equilibrium constrained optimization problems

In this paper, a feedback neural network model is proposed to compute the solution of the mathematical programs with equilibrium constraints (MPEC). The MPEC problem is altered into an identical one-level non-smooth optimization problem, then a sequential dynamic scheme that progressively approximates the non-smooth problem is presented. Besides asymptotic stability, it is proven that the limit equilibrium point of the suggested dynamic model is a solution for the original MPEC problem. Numerical simulation of various types of MPEC problems shows the significance of the results. Moreover, the scheme is applied to compute the Stackelberg-Cournot-Nash equilibria.