Compactness Properties, Openness Criteria and Coderivatives |
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Authors: | Jean-Paul Penot |
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Institution: | (1) Faculté des Sciences, University of Pau, Mathématiques, URA CNRS 1204, Av. de l'Université, 64000 Pau, France |
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Abstract: | We study the local surjectivity and openness properties of mappings and correspondences by using coderivatives. We recall local criteria but concentrate on point criteria. Our study relies on a compactness condition which is of independent interest, for instance, for the study of the behavior of the injectivity constant of a linear map or of a convex process under stabilization procedures. Several known criteria for openness are shown to be a consequences of this new compactness condition. |
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Keywords: | coderivative coderivatively compact compactness injectivity normal compactness openness nonsmooth analysis subdifferential |
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