In this presentation, we discuss a new method by Siddiqui and Gabriel (2012) to solve mathematical programs with equilibrium constraints (MPEC). It is based on decomposing the complementarity conditions of the lower-level problem (optimization or equilibrium) using SOS1 variables. As such, the approach represents an improvement over the previous SOS2 decomposition of bilinear terms (Gabriel et al., 2006). Several versions of the SOS1 method are presented along with theoretical and numerical results with an application to energy.
 S.A. Gabriel, R. Garcia-Bertrand, P. Sahakij, A. Conejo. 2006. "A Practical Approach in Approximately Bilinear Functions in Mathematical Programming Problems by Using Schur's Decomposition and SOS Type 2 Variables," Journal of the Operational Research Society, 57, 995-1004.
 S. Siddiqui and S.A. Gabriel. 2012. "An SOS-Based Approach for Solving MPECS with a Natural Gas Application," Networks and Special Economics, 1-23.