On mappings covering at a nonlinear rate and their perturbation stability |
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Authors: | A Uderzo |
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Institution: | Department of Statistics, University of Milano-Bicocca, Via Bicocca degli Arcimboldi, 8-20126 Milan, Italy |
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Abstract: | The present paper contains a study of covering (alias, openness) properties at a nonlinear rate for set-valued mappings between metric spaces. Such study is focussed on the stability of these properties in the presence of perturbations. A crucial result valid for linear openness, known as Milyutin’s theorem, is extended to set-valued mappings covering at a nonlinear rate under possibly non-Lipschitz perturbations. Consequently, a Lyusternik type theorem is derived from such extension and a general penalization principle for constrained optimization problems, which exploits nonlinear covering properties, is presented. |
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Keywords: | primary 49J53 secondary 46A30 47H04 49J52 90C48 |
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