Minimum mean-squared deviation method for stochastic complementarity problems

Abstract

In this paper, we propose a new reformulation for stochastic complementarity problems (SCPs). The new formulation is based on the minimum mean-squared deviation rule in statistics. Under mild conditions, we prove the existence of the solution of the new reformulation for SCP. Furthermore, we present a smoothing sample average approximation method for solving the problems. The convergence properties of the optimal solutions of the approximation problems are studied under mild conditions. Finally, some numerical results are listed as well.

Keywords:

• stochastic complementarity problems
• minimum mean-squared deviation
• sample average approximation method
• complementarity function
• smoothing technique

2010 AMS Subject Classifications:

• 90C15
• 90C33

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [Grant No. 11401384], the Scientific Research Foundation for youth teachers of Lixin University of Commerce [Grant No. 2014QNYB17].