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October  2019, 15(4): 1653-1675. doi: 10.3934/jimo.2018116

Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China 2 School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, China

* Corresponding author: Fanyun Meng

Received  February 2017 Revised  May 2018 Published  August 2018

Fund Project: The research is partially supported by Huzhou science and technology plan on No.2016GY03, the Natural Science Foundation of China, Grant 11601061.

We consider the sample average approximation method for a stochastic multiobjective programming problem constrained by parametric variational inequalities. The first order necessary conditions for the original problem and its sample average approximation (SAA) problem are established under constraint qualifications. By graphical convergence of set-valued mappings, the stationary points of the SAA problem converge to the stationary points of the true problem when the sample size tends to infinity. Under proper assumptions, the convergence of optimal solutions of SAA problems is also obtained. The numerical experiments on stochastic multiobjective optimization problems with variational inequalities are given to illustrate the efficiency of SAA estimators.

Citation: Liping Pang, Fanyun Meng, Jinhe Wang. Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1653-1675. doi: 10.3934/jimo.2018116
References:

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References:
Convergence of SAA optimal values
Convergence of SAA optimal solutions
The boundary of set $\mathbb{E}[\phi(C,\cdot)]$
Convergence of SAA optimal values
Convergence of SAA optimal solutions
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