Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems
Abstract This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for ro...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03315-5 |
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| _version_ | 1849434042365116416 |
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| author | Shan Cai Xiaoping Li |
| author_facet | Shan Cai Xiaoping Li |
| author_sort | Shan Cai |
| collection | DOAJ |
| description | Abstract This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for robust approximate quasi-weakly efficient solutions using the Clarke subdifferential. Subsequently, we present a sufficient optimality condition for such solutions under the assumption of approximate generalized convexity. Finally, we formulate two scalarization theorems for robust approximate quasi-weakly efficient solutions by employing a cone-strongly monotonic function. The definitions and main conclusions of this paper are supported by specific examples. |
| format | Article |
| id | doaj-art-3ee4ca824db54500a56e52dc32da47ae |
| institution | Kabale University |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-3ee4ca824db54500a56e52dc32da47ae2025-08-20T03:26:48ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-06-012025111610.1186/s13660-025-03315-5Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problemsShan Cai0Xiaoping Li1College of Mathematics and Imformation Science, Xiangnan UniversityCollege of Mathematics and Imformation Science, Xiangnan UniversityAbstract This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for robust approximate quasi-weakly efficient solutions using the Clarke subdifferential. Subsequently, we present a sufficient optimality condition for such solutions under the assumption of approximate generalized convexity. Finally, we formulate two scalarization theorems for robust approximate quasi-weakly efficient solutions by employing a cone-strongly monotonic function. The definitions and main conclusions of this paper are supported by specific examples.https://doi.org/10.1186/s13660-025-03315-5Semi-infinite vector equilibriumOptimality conditionClarke subdifferentialScalarization theoremsCone strongly monotone function |
| spellingShingle | Shan Cai Xiaoping Li Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems Journal of Inequalities and Applications Semi-infinite vector equilibrium Optimality condition Clarke subdifferential Scalarization theorems Cone strongly monotone function |
| title | Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems |
| title_full | Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems |
| title_fullStr | Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems |
| title_full_unstemmed | Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems |
| title_short | Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems |
| title_sort | optimality and scalarization of robust approximate solutions for semi infinite vector equilibrium problems |
| topic | Semi-infinite vector equilibrium Optimality condition Clarke subdifferential Scalarization theorems Cone strongly monotone function |
| url | https://doi.org/10.1186/s13660-025-03315-5 |
| work_keys_str_mv | AT shancai optimalityandscalarizationofrobustapproximatesolutionsforsemiinfinitevectorequilibriumproblems AT xiaopingli optimalityandscalarizationofrobustapproximatesolutionsforsemiinfinitevectorequilibriumproblems |