Liu, Yongchao, Xu, Huifu and Ye, Jane J.
Penalized sample average approximation methods for stochastic mathematical programs with complementarity constraints
Mathematics of Operations Research, 36, (4), .
This paper considers a one-stage stochastic mathematical program with a complementarity
constraint (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 must
be made before the realization of the uncertainties. A partially exactly penalized sample average
approximation (SAA) scheme is proposed to solve the problem. Asymptotic convergence of optimal
solutions and stationary points of the penalized SAA problem is carried out. It is shown under
some moderate conditions that the statistical estimators obtained from solving the penalized SAA
problems converge almost surely to its true counterpart as the sample size increases.
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