Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints

Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints

0.00 Avg rating0 Votes
Article ID: iaor201111568
Volume: 36
Issue: 4
Start Page Number: 670
End Page Number: 694
Publication Date: Nov 2011
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: programming: probabilistic
Abstract:

This paper considers a one‐stage stochastic mathematical program with a complementarity constraint (SMPCC), where uncertainties appear in both the objective function and the complementarity 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. Exponential rate of convergence of estimators is also established under some additional conditions.

Reviews

Required fields are marked *. Your email address will not be published.