Abstract

This paper proposes a new decomposition method for globally solvingmathematical programming problems with affine equilibrium constraints (AMPEC).First, we view AMPEC as a bilevel programming problem where the lower one isa parametric affine variational inequality. Then we use a regularization techniqueto formulate the resulting problem as a mathematical program with an additionalconstraint defined by the difference of two convex functions (DC function). A mainfeature of this DC decomposition is that the second component depends upon onlythe parameter in the lower problem. This property allows us to develop branch-and-bound algorithms for globally solving AMPEC where the adaptive rectangularbisection takes place only in the space of the parameter. As an example, we usethe proposed algorithm to solve a bilevel Nash-Cournot equilibrium market model.Computational results show the efficiency of the proposed algorithm