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Journal Articles Journal of Convex Analysis Year : 2005

Filling the Gap Between Lower-C1 and Lower-C2 Functions


The classes of lower-C1,α functions (0 < α ≤ 1), that is, functions locally representable as a maximum of a compactly parametrized family of continuously differentiable functions with α-H ̈older derivative, are hereby introduced. These classes form a strictly decreasing sequence from the larger class of lower-C1 towards the smaller class of lower-C2 functions, and can be analogously characterized via perturbed con- vex inequalities or via appropriate generalized monotonicity properties of their subdifferentials. Several examples are provided and a complete classification is given.
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hal-00804407 , version 1 (25-03-2013)


  • HAL Id : hal-00804407 , version 1


Aris Daniilidis, Jérôme Malick. Filling the Gap Between Lower-C1 and Lower-C2 Functions. Journal of Convex Analysis, 2005, 12 (2), pp.315-329. ⟨hal-00804407⟩
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