Abstract

A general abstract duality result is proposed for equations which are governed by the sum of two operators (possibly multivalued). It allows to unify a large number of variational duality principles, including the Clarke-Ekeland least dual action principle and the Singer-Toland duality. Moreover, it offers a new duality approach to some central questions in the theory of variational inequalities and maximal monotone operators.

Author information

Contact details are reproduced from the original publication and may be historical.

H. Attouch

Laboratoire d’Analyse Convexe, Université Montpellier II, 34095 Montpellier Cedex 5, France.

M. Théra

LACO, URA-CNRS 1586, Université de Limoges, 87060 Limoges Cedex, France

Keywords

  • Abstract duality principle
  • Clarke-Ekeland duality
  • Hamiltonian systems
  • Fenchel-Moreau-Rockafellar duality
  • Singer-Toland duality
  • Robinson normal mappings
  • maximal monotone operators
  • convex subdifferential operator
  • qualification conditions

Suggested citation

H. Attouch, M. Théra. “A General Duality Principle for the Sum of Two Operators.” Journal of Convex Analysis 3 (1996), No. 1, 1–24. https://doi.org/10.68381/jca03001

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Published by Heldermann Verlag, 1996. Rights now held by Banach Press.