A SNCP Method for Solving Equilibrium Problems with Equilibrium Constraints

This paper studies algorithms for equilibrium problems with equilibrium constraints (EPECs). We present a generalization of Scholtes’s regularization scheme for MPECs and extend his convergence results to this new relaxation method. We propose a sequential nonlinear complementarity (SNCP) algorithm to solve EPECs and establish the convergence of this algorithm. We present numerical results comparing the SNCP algorithm and diagonalization (nonlinear Gauss- Seidel and nonlinear Jacobi) methods on randomly generated EPEC test problems. The computational experience to date shows that both the SNCP algorithm and the nonlinear Gauss-Seidel method outperform the nonlinear Jacobi method