Zeitschrift für Operations Research

, Volume 42, Issue 1, pp 109–125 | Cite as

Subdifferentials with respect to dualities

  • Juan-Enrique Martinez-Legaz
  • Ivan Singer


LetX andW be two sets andΔ: ¯RX → ¯RW a duality (i.e., a mapping\(\Delta :f \in \bar R^X \to f^\Delta \in \bar R^W \) such that\(\left( {\mathop {\inf f_i }\limits_{i \in I} } \right)^\Delta = \mathop {\sup }\limits_{i \in I} f_i^\Delta \) for all\(\{ f_i \} _{i \in I} \subseteq \bar R^X \) and all index setsI). We introduce and study the subdifferential\(\partial ^\Delta f(x_0 )\) of a function\(f \in \bar R^X \) at a pointxo∈ X, with respect toΔ. We also consider the particular cases whenΔ is a (Fenchel-Moreau) conjugation, or a ∨ -duality, or a ⊥-duality, in the sense of [8].

Key Words

Dualities generalized subdifferentials conjugations 


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Copyright information

© Physica-Verlag 1995

Authors and Affiliations

  • Juan-Enrique Martinez-Legaz
    • 1
  • Ivan Singer
    • 2
  1. 1.Dept. Economia i Historia EconomicaUniversitat Autonoma de BarcelonaBarcelonaSpain
  2. 2.Institute of Mathematics of the Romanian AcademyBucharestRomania

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