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

Gui Hua Lin; Mei Ju Luo; Jin Zhang

doi:10.1007/s10898-016-0413-9

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

Gui Hua Lin, Mei Ju Luo^*, Jin Zhang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

37 Downloads (Pure)

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.

Original language	English
Pages (from-to)	487-510
Number of pages	24
Journal	Journal of Global Optimization
Volume	66
Issue number	3
DOIs	https://doi.org/10.1007/s10898-016-0413-9
Publication status	Published - 1 Nov 2016

Scopus Subject Areas

Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

User-Defined Keywords

Non-smoothness
Sample average approximation
Smoothing
Stochastic mathematical program with equilibrium constraints

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10.1007/s10898-016-0413-9

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Cite this

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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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N2 - 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.

AB - 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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KW - Sample average approximation

KW - Smoothing

KW - Stochastic mathematical program with equilibrium constraints

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JO - Journal of Global Optimization

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

Abstract

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