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

Gui-Hua Lin (), Mei-Ju Luo () and Jin Zhang ()
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Gui-Hua Lin: Shanghai University
Mei-Ju Luo: Liaoning University
Jin Zhang: Hong Kong Baptist University

Journal of Global Optimization, 2016, vol. 66, issue 3, No 6, 487-510

Abstract: 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.

Keywords: Non-smoothness; Smoothing; Sample average approximation; Stochastic mathematical program with equilibrium constraints; 90C15; 90C30; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10898-016-0413-9

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