Abstract

The asymptotical limit of the trajectory defined by the continuous steepest descent method for a proper closed convex function f on a Hilbert space is characterized in the set of minimizers of f via an asymptotical variational principle of Brezis-Ekeland type. The implicit discrete analogue (prox method) is also considered.

Author information

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

B. Lemaire

Université Montpellier II, Place E. Bataillon, 34095 Montpellier Cedex 5, France

Keywords

  • Asymptotical
  • convex minimization
  • differential inclusion
  • prox method
  • steepest descent
  • variational principle

Suggested citation

B. Lemaire. “An Asymptotical Variational Principle Associated with the Steepest Descent Method for a Convex Function.” Journal of Convex Analysis 3 (1996), No. 1, 63–70. https://doi.org/10.68381/jca03005

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