A class of stochastic mathematical programs with complementarity constraints: Reformulations and algorithms

We consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs), in which all decisions are required to be made here-and-now, before a random event is observed. We show that this kind of SMPEC plays a very important role in practice. In order to develop effective algorithms, we first give some reformulations of the SMPEC and then, based on these reformulations, we propose a smoothed penalty approach for solving the problem. A comprehensive convergence theory is also included.