Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems
In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk c...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/1203627 |
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| author | Meiju Luo Kun Zhang |
| author_facet | Meiju Luo Kun Zhang |
| author_sort | Meiju Luo |
| collection | DOAJ |
| description | In this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given. |
| format | Article |
| id | doaj-art-01f9cbdc6dbe46adba2128bfaeeed7bf |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-01f9cbdc6dbe46adba2128bfaeeed7bf2025-08-20T03:22:27ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/12036271203627Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality ProblemsMeiju Luo0Kun Zhang1School of Mathematics, Liaoning University, Shenyang, Liaoning 110036, ChinaSchool of Mathematics, Liaoning University, Shenyang, Liaoning 110036, ChinaIn this paper, we consider stochastic vector variational inequality problems (SVVIPs). Because of the existence of stochastic variable, the SVVIP may have no solutions generally. For solving this problem, we employ the regularized gap function of SVVIP to the loss function and then give a low-risk conditional value-at-risk (CVaR) model. However, this low-risk CVaR model is difficult to solve by the general constraint optimization algorithm. This is because the objective function is nonsmoothing function, and the objective function contains expectation, which is not easy to be computed. By using the sample average approximation technique and smoothing function, we present the corresponding approximation problems of the low-risk CVaR model to deal with these two difficulties related to the low-risk CVaR model. In addition, for the given approximation problems, we prove the convergence results of global optimal solutions and the convergence results of stationary points, respectively. Finally, a numerical experiment is given.http://dx.doi.org/10.1155/2020/1203627 |
| spellingShingle | Meiju Luo Kun Zhang Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems Complexity |
| title | Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems |
| title_full | Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems |
| title_fullStr | Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems |
| title_full_unstemmed | Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems |
| title_short | Convergence Analysis of the Approximation Problems for Solving Stochastic Vector Variational Inequality Problems |
| title_sort | convergence analysis of the approximation problems for solving stochastic vector variational inequality problems |
| url | http://dx.doi.org/10.1155/2020/1203627 |
| work_keys_str_mv | AT meijuluo convergenceanalysisoftheapproximationproblemsforsolvingstochasticvectorvariationalinequalityproblems AT kunzhang convergenceanalysisoftheapproximationproblemsforsolvingstochasticvectorvariationalinequalityproblems |