Prox-regular functions in variational analysis |
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| Authors: | R. A. Poliquin R. T. Rockafellar |
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| Affiliation: | Deptartment of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 ; Department of Mathematics, University of Washington, Seattle, Washington 98195 |
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| Abstract: | The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not. |
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| Keywords: | Prox-regularity amenable functions primal-lower-nice functions proximal mappings Moreau envelopes regularization subgradient mappings nonsmooth analysis variational analysis proto-derivatives second-order epi-derivatives Attouch's theorem |
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