Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

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

Publication Date

11-2016

Source Publication Title

Journal of Global Optimization

Volume

66

Issue

3

Start Page

487

End Page

510

Publisher

Springer Verlag

Peer Reviewed

1

Copyright

The final publication is available at Springer via http://dx.doi.org/10.1007/s10898-016-0413-9

Funder

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.

DOI

10.1007/s10898-016-0413-9

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10898-016-0413-9

ISSN (print)

09255001

ISSN (electronic)

15732916

Available for download on Friday, December 01, 2017

Included in

Mathematics Commons

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