WIAS Preprint No. 2004, (2014)

Second-order subdifferential of 1- and maximum norm


  • Emich, Konstantin

2010 Mathematics Subject Classification

  • 49J52 49J53


  • second-order subdifferential, polyhedral norms




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.

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