Vol.2 No.3 (August 2012)
Some Results on Solving a Class of Stochastic Mathematical Programs with Complementarity Constraints
This paper considers a class of stochastic linear programs with linear complementarity constraints (SLPCC). We first transform the SLPCC into a stochastic linear programming problem under some conditions. Then, we suggest a sampling average approximation method to solve the SLPCC and establish its conver-gence analysis. We finally report some preliminary numerical results.
黄玉文 , 林贵华 (2012) 求解一类随机互补约束数学规划问题的若干结果。 运筹与模糊学， 2， 35-41. doi: 10.12677/ORF.2012.23005
 M. Fukushima, G.-H. Lin. Smoothing methods for mathematical programs with equilibrium constraints. Proceedings of the ICKS’04, IEEE Computer Society, 2004: 206-213.
 Z.-Q. Luo, J.-S. Pang and D. Ralph. Mathematical programs with equilibrium constraints. Cambridge: Cambridge University Press, 1996. J. Outrata, M. Kocvara and J. Zowe. Nonsmooth approach to optimization problems with equilibrium constraints. Dordrecht: Kluwer Aca-demic Publishers, 1998.
 H. Scheel, S. Scholtes. Mathematical programs with complementarity constraints: Stationarity, optimality, and sensitivity. Mathematics of Operations Research, 2000, 25(1): 1-22.
 F. Facchinei, J.-S. Pang. Finite-dimensional variational inequalities and complementarity problems. New York: Springer-Verlag, 2003.
 R. W. Cottle, J.-S. Pang and R. E. Stone. The linear complementarity problem. Boston: Academic Press, 1992.
 X. Chen, S. Xiang. Impicit solution function of P0 and Z matrix linear complementarity constraints. Mathematical Programming, 2011, 128(1- 2): 1-18.
 J. Hu, J. E. Mitchell, J.-S. Pang, K. P. Bennett and G. Kunapuli. On the global solution of linear programs with linear complementarity con- straints. SIAM Journal on Optimization, 2009, 19(1): 445-471.
 韩继业, 修乃华, 戚厚铎. 非线性互补理论与算法[M]. 上海: 上海科学技术出版社, 2006.
 A. Ruszczynski, A. Shapiro. Stochastic programming. Handbooks in operations research and management science. Amsterdam: Elsevier, 2003.