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| Volume 4, Number 3, September 2008, pp. 621-628 | |||||||||
| Michel Volle |
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| Key words: | |||||||||
| subdifferential calculus, argmin calculus, convex analysis, Legendre-Fenchel conjugate Kuratowski-Painlevé convergence | |||||||||
| Mathematices Subject Classification: 90C25, 90C26, 49N15 | |||||||||
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| Abstract: | |||
| Convex subdifferential calculus obeys various rules possibly involving approximate sub-differentials. Some of these rules concern nonconvex functions like for instance the difference of convex functions. In this note we point out a formula for the subdifferential of the lower semicontinuous hull of an arbitrary extended real-valued function h. We apply the result to the case when h is the infimal convolution of functions that need not be convex. The symmetric approach in terms of minimum sets of functions is also investigate and argmin calculus rules are obtained. We derive from this approach the Hiriart-Urruty and Phelps formula on the sum of two proper lower semicontinuous convex functions and provide a remarkable topological stability property of this formula. | |||
| Complements on subdifferential calculus | ||