Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints

This paper considers a one-stage stochastic mathematical program with a complementarityconstraint (SMPCC) where uncertainties appear in both the objective function and the comple-mentarity constraint, and an optimal decision on both upper and lower level decision variables mustbe made before the realization of the uncertainties. A partially exactly penalized sample averageapproximation (SAA) scheme is proposed to solve the problem. Asymptotic convergence of optimalsolutions and stationary points of the penalized SAA problem is carried out. It is shown undersome moderate conditions that the statistical estimators obtained from solving the penalized SAAproblems converge almost surely to its true counterpart as the sample size increases