Gap Continuity of Multimaps |
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Authors: | Jean-Paul Penot |
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Affiliation: | (1) Faculté des Sciences, Université de Pau, Mathématiques UMR CNRS 5142, B.P. 1155, 64013 PAU Cedex, France |
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Abstract: | We introduce a notion of continuity for multimaps (or set-valued maps) which is mild. It encompasses both lower semicontinuity and upper semicontinuity. We give characterizations and we consider some permanence properties. This notion can be used for various purposes. In particular, it is used for continuity properties of subdifferentials and of value functions in parametrized optimization problems. We also prove an approximate selection theorem. |
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Keywords: | Correspondence Gap-continuity Lower semicontinuity Multimap Multifunction Multimapping Set-valued map Subdifferential Semicontinuity Value function |
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