| Autor: |
Barbara, A, Jourani, A |
| Přispěvatelé: |
Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB) |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Popis: |
This paper deals with error bound characterizations of Guignard's qualification condition for a convex inequality system in a Banach space X. We establish necessary and sufficient conditions for a closed convex set S defined by a convex function g to have Guignard's condition. These conditions are expressed in terms of the notion of error bound. Our results show that these characterizations hlod in the following special cases: 1. g is the maximum of a finite number of differentiable convex functions. 2. S is closed convex and polyhedral. 3. The dimension of the subspace lin(S) is less than 2 and g is positively homogeneous. We construct technical examples showing that these characterizations are limited to the three situations above. We introduce a new condition in terms of the gauge function which allows us to give an error bound characterization of convex nondifferentiable systems and to obtain as a direct consequence different characterizations of the concept of strong conical hull intersection property (CHIP) for a finite collection of convex sets. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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