ASYMPTOTIC CONVERGENCE OF STATIONARY POINTS OF STOCHASTIC MULTIOBJECTIVE PROGRAMS WITH PARAMETRIC VARIATIONAL INEQUALITY CONSTRAINT VIA SAA APPROACH

作者：Pang, Liping; Meng, Fanyun^*; Wang, Jinhe

来源：Journal of Industrial and Management Optimization, 2019, 15(4): 1653-1675.

DOI：10.3934/jimo.2018116

• Stochastic programming
• multiobjective programming
• parametric variational inequalities
• sample average approximation

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.

• 出版日期2019-10
• 单位大连理工大学; 青岛理工大学