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Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints

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Abstract

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.

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Acknowledgments

The authors are grateful to two anonymous referees whose helpful suggestions have led to much improvement of the paper. We are also grateful to Professor Jane Ye for her invaluable help with many aspects of this paper.

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Authors and Affiliations

  1. School of Management, Shanghai University, Shanghai, China

    Gui-Hua Lin

  2. School of Mathematics, Liaoning University, Liaoning, China

    Mei-Ju Luo

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

    Jin Zhang

Authors
  1. Gui-Hua Lin
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  2. Mei-Ju Luo
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  3. Jin Zhang
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Corresponding author

Correspondence to Mei-Ju Luo.

Additional information

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.

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Lin, GH., Luo, MJ. & Zhang, J. Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints. J Glob Optim 66, 487–510 (2016). https://doi.org/10.1007/s10898-016-0413-9

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  • DOI: https://doi.org/10.1007/s10898-016-0413-9

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