Second-order subdifferential of 1- and maximum norm
Please always quote using this URN:urn:nbn:de:0296-matheon-13231
- We derive formulae for the second-order subdifferential of polyhedral norms. These formulae are fully explicit in terms of initial data. In a first step we rely on the explicit formula for the coderivative of normal cone mapping to polyhedra. Though being explicit, this formula is quite involved and difficult to apply. Therefore, we derive simple formulae for the 1-norm and - making use of a recently obtained formula for the second-order subdifferential of the maximum function - for the maximum norm.
Author: | Konstantin Emich |
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URN: | urn:nbn:de:0296-matheon-13231 |
Referee: | Rene Henrion |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2014/07/24 |
Release Date: | 2014/07/24 |
Tag: | Second-order subdifferential; polyhedral norms |
Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J52 Nonsmooth analysis [See also 46G05, 58C50, 90C56] |
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J53 Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] | |
Preprint Number: | 1069 |