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ISSN 1088-6850(e) ISSN 0002-9947(p)

Prox-regular functions in variational analysis

Author(s): R. A. Poliquin; R. T. Rockafellar
Journal: Trans. Amer. Math. Soc. 348 (1996), 1805-1838.
MSC (1991): Primary 49A52, 58C06, 58C20; Secondary 90C30
MathSciNet review: 1333397
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Abstract: The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- $\mathcal{C}^{2}$ 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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