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Type: Text × Subject: Subdifferential ×

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    Error bounds: necessary and sufficient conditions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Fabian, Marian J.; Henrion, Ren´e; Kruger, Alexander Y.; Outrata, Jiˇr´ı
    The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.
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    A simple formula for the second-order subdifferential of maximum functions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Emich, Konstantin; Henrion, René
    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 secondorder subdifferentials.