WIAS Preprint No. 1819, (2013)

A simple formula for the second-order subdifferential of maximum functions



Authors

  • Emich, Konstantin
  • Henrion, René

2010 Mathematics Subject Classification

  • 49J52 49J53

Keywords

  • second-order subdifferential, extended partial second-order subdifferential, maximum function, calculus rules

Abstract

We derive a simple formula for the second-order subdifferential of the maximum of coordinates which allows us to construct this set immediately from its argument and the direction to which it is applied. This formula can be combined with a chain rule recently proved by Mordukhovich and Rockafellar [9] in order to derive a similarly simple formula for the extended partial second-order subdifferential of finite maxima of smooth functions. Analogous formulae can be derived immediately for the full and conventional partial second-order subdifferentials.

Appeared in

  • Vietnam J. Math., 42 (2014) pp. 467--478.

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