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

Li-Ping Pang | Zendy; Fanyun Meng | Zendy; Jinhe Wang | Zendy

Open Access

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

Author(s) -

Li-Ping Pang,

Fanyun Meng,

Jinhe Wang

Publication year - 2018

Publication title -

journal of industrial and management optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.325

H-Index - 32

eISSN - 1553-166X

pISSN - 1547-5816

DOI - 10.3934/jimo.2018116

Subject(s) - mathematics , convergence (economics) , mathematical optimization , parametric statistics , constraint (computer aided design) , variational inequality , estimator , stationary point , infinity , stochastic programming , mathematical analysis , statistics , geometry , economics , economic growth

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.

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