Sample average approximation method for a class of stochastic vector variational inequalities

被引：0

作者：

Dong, Dan-dan ^{[1
,2
]}

Liu, Jian-xun ^{[3
]}

Tang, Guo-ji ^{[4
]}

机构：

[1] Guangxi Minzu Univ, Sch Math & Phys, Nanning, Peoples R China

[2] Henan Univ Sci & Technol, Business Sch, Luoyang, Peoples R China

[3] Guangxi Minzu Univ, Ctr Appl Math Guangxi, Sch Math & Phys, Nanning, Peoples R China

[4] Guangxi Minzu Univ, Ctr Appl Math Guangxi, Sch Math & Phys, Guangxi Key Lab Hybrid Computat & IC Design Anal, Nanning, Peoples R China

来源：

APPLICABLE ANALYSIS | 2024年 / 103卷 / 09期

基金：

中国国家自然科学基金;

关键词：

J; Tugaut; Stochastic vector variational inequality; regularized gap function; sample average approximation; convergence; RESIDUAL MINIMIZATION METHOD; GAP FUNCTION; CONSTRAINTS;

D O I：

10.1080/00036811.2023.2260403

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, the expected-value (EV) reformulation of a class of stochastic vector variational inequalities (SVVI) is investigated. By using the regularized gap function, the EV reformulation of SVVI is transformed into a constrained optimization problem. Then a sample average approximation (SAA) method is proposed for solving the constrained optimization problem. Under suitable assumptions, the limiting behaviors of the optimal values and optimal solutions of the approximation problem are investigated. Finally, the rates of convergence in the different senses of optimal solutions for sample average approximation problem are discussed under the error bound condition.

引用

页码：1649 / 1668

页数：20

共 49 条

[11]

Facchinei F, 2003, Springer Series in Operations Research, VI and II

[12] EQUIVALENT DIFFERENTIABLE OPTIMIZATION PROBLEMS AND DESCENT METHODS FOR ASYMMETRIC VARIATIONAL INEQUALITY PROBLEMS [J].

FUKUSHIMA, M .

MATHEMATICAL PROGRAMMING, 1992, 53 (01) :99-110

[13]

Giannessi F., 1980, Variational Inequality and Complimentary Problems, P151

[14]

GIANNESSI F, 2000, VECTOR VARIATIONAL I, V38

[15] Sample-path solution of stochastic variational inequalities [J].

Gürkan, G ;

Özge, AY ;

Robinson, SM .

MATHEMATICAL PROGRAMMING, 1999, 84 (02) :313-333

[16] ON SOME NON-LINEAR ELLIPTIC DIFFERENTIAL-FUNCTIONAL EQUATIONS [J].

HARTMAN, P ;

STAMPACCHIA, G .

ACTA MATHEMATICA UPPSALA, 1966, 115 (3-4) :271-+

[17] A SAMPLE AVERAGE APPROXIMATION METHOD BASED ON A D-GAP FUNCTION FOR STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS [J].

He, Suxiang ;

Zhang, Pan ;

Hu, Xiao ;

Hu, Rong .

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2014, 10 (03) :977-987

[18] Weak sharpness for gap functions in vector variational inequalities [J].

Huang, N. J. ;

Li, J. ;

Yang, X. Q. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (02) :449-457

[19] Stochastic approximation approaches to the stochastic variational inequality problem [J].

Jiang, Houyuan ;

Xu, Huifu .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (06) :1462-1475

[20]

Jiang J., PREPRINT OPTIMIZATIO

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