Relaxation approach for equilibrium problems with equilibrium constraints

Abstract

We study a generalization of the relaxation scheme for mathematical programs with equilibrium constraints (MPECs) studied in Steffensen and Ulbrich (2010) [31] to equilibrium problems with equilibrium constraints (EPECs). This new class of optimization problems arise, for example, as reformulations of bilevel models used to describe competition in electricity markets. The convergence results of Steffensen and Ulbrich (2010) [31] are extended to parameterized MPECs and then further used to prove the convergence of the associated method for EPECs. Moreover, the proposed relaxation scheme is used to introduce and discuss a new relaxed sequential nonlinear complementarity method to solve EPECs. Both approaches are numerically tested and compared to existing diagonalization and complementarity approaches on a randomly generated test set.