- Title
- A uniform approach to hölder calmness of subdifferentials
- Creator
- Beer, Gerald; Cánovas, Maria; López, Marco; Parra, Juan
- Date
- 2020
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/173718
- Identifier
- vital:14705
- Identifier
- ISBN:0944-6532 (ISSN)
- Abstract
- For finite-valued convex functions f defined on the n-dimensional Euclidean space, we are interested in the set-valued mapping assigning to each pair (f, x) the subdifferential of f at x. Our approach is uniform with respect to f in the sense that it involves pairs of functions close enough to each other, but not necessarily around a nominal function. More precisely, we provide lower and upper estimates, in terms of Hausdorff excesses, of the subdifferential of one of such functions at a nominal point in terms of the subdifferential of nearby functions in a ball centered in such a point. In particular, we obtain the (1/2) - Hölder calmness of our mapping at a nominal pair (f, x) under the assumption that the subdifferential mapping viewed as a set-valued mapping from Rn to Rn with f fixed is calm at each point of {x} × ∂f(x). © Heldermann Verlag; Funding details: Australian Research Council, ARC, DP160100854 Funding details: European Commission, EU Funding details: Ministerio de Economía y Competitividad, MINECO Funding details: Federación Española de Enfermedades Raras, FEDER Funding text 1:
- Publisher
- Heldermann Verlag
- Relation
- Journal of Convex Analysis Vol. 27, no. 1 (2020), p.; http://purl.org/au-research/grants/arc/DP160100854
- Rights
- Copyright Heldermann Verlag
- Rights
- This metadata is freely available under a CCO license
- Subject
- Convex functions; Hausdorff excess; Hölder calmness; Sudifferentials; Uniform spaces
- Reviewed
- Funder
- Funding details: Australian Research Council, ARC, DP160100854 Funding details: European Commission, EU Funding details: Ministerio de Economía y Competitividad, MINECO Funding details: Federación Española de Enfermedades Raras, FEDER Funding text 1:
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