Department of Mathematics
We consider a stochastic non-smooth programming problem with equality, inequality and abstract constraints, which is a generalization of the problem studied by Xu and Zhang (Math Program 119:371–401, 2009) where only an abstract constraint is considered. We employ a smoothing technique to deal with the non-smoothness and use the sample average approximation techniques to cope with the mathematical expectations. Then, we investigate the convergence properties of the approximation problems. We further apply the approach to solve the stochastic mathematical programs with equilibrium constraints. In addition, we give an illustrative example in economics to show the applicability of proposed approach.
Non-smoothness, Smoothing, Sample average approximation, Stochastic mathematical program with equilibrium constraints
Source Publication Title
Journal of Global Optimization
The final publication is available at Springer via http://dx.doi.org/10.1007/s10898-016-0413-9
This work was supported in part by the NSFC (No. 11431004, No. 11501275), the Humanity and Social Science Foundation of Ministry of Education of China (No. 15YJA630034), the Innovation Program of Shanghai Municipal Education Commission (No. 14ZS086), the Scientific Research Fund of Liaoning Provincial Education Department (No. L2015199), the Hongkong Baptist University FRG1/15-16/027 and RC-NACAN-ZHANG J.
Link to Publisher's Edition
Lin, G., Luo, M., & Zhang, J. (2016). Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints. Journal of Global Optimization, 66 (3), 487-510. https://doi.org/10.1007/s10898-016-0413-9