Weighted Method for Uncertain Nonlinear Variational Inequality Problems
A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the converge...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/10/974 |
| _version_ | 1818411136862650368 |
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| author | Cunlin Li Mihai Postolache Zhifu Jia |
| author_facet | Cunlin Li Mihai Postolache Zhifu Jia |
| author_sort | Cunlin Li |
| collection | DOAJ |
| description | A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity. |
| first_indexed | 2024-12-14T10:26:37Z |
| format | Article |
| id | doaj.art-f4375841783a4873904e6b43f9bd7908 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-14T10:26:37Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f4375841783a4873904e6b43f9bd79082022-12-21T23:06:19ZengMDPI AGMathematics2227-73902019-10-0171097410.3390/math7100974math7100974Weighted Method for Uncertain Nonlinear Variational Inequality ProblemsCunlin Li0Mihai Postolache1Zhifu Jia2Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, ChinaCenter for General Education, China Medical University, Taichung 40402, TaiwanState Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaA convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.https://www.mdpi.com/2227-7390/7/10/974uncertain variational inequalityuwerm problemconvergence analysis |
| spellingShingle | Cunlin Li Mihai Postolache Zhifu Jia Weighted Method for Uncertain Nonlinear Variational Inequality Problems Mathematics uncertain variational inequality uwerm problem convergence analysis |
| title | Weighted Method for Uncertain Nonlinear Variational Inequality Problems |
| title_full | Weighted Method for Uncertain Nonlinear Variational Inequality Problems |
| title_fullStr | Weighted Method for Uncertain Nonlinear Variational Inequality Problems |
| title_full_unstemmed | Weighted Method for Uncertain Nonlinear Variational Inequality Problems |
| title_short | Weighted Method for Uncertain Nonlinear Variational Inequality Problems |
| title_sort | weighted method for uncertain nonlinear variational inequality problems |
| topic | uncertain variational inequality uwerm problem convergence analysis |
| url | https://www.mdpi.com/2227-7390/7/10/974 |
| work_keys_str_mv | AT cunlinli weightedmethodforuncertainnonlinearvariationalinequalityproblems AT mihaipostolache weightedmethodforuncertainnonlinearvariationalinequalityproblems AT zhifujia weightedmethodforuncertainnonlinearvariationalinequalityproblems |