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

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

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Article ID: iaor20163641
Volume: 66
Issue: 3
Start Page Number: 487
End Page Number: 510
Publication Date: Nov 2016
Journal: Journal of Global Optimization
Authors: , ,
Keywords: stochastic processes, heuristics, programming: mathematical
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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