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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03315-5 |
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| Summary: | 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. |
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| ISSN: | 1029-242X |