JournalsrmiVol. 27, No. 2pp. 449–474

The ε\varepsilon-strategy in variational analysis: illustration with the closed convexification of a function

  • Jean-Baptiste Hiriart-Urruty

    Université Paul Sabatier, Toulouse, France
  • Marco A. López

    Alicante University, Spain
  • Michel Volle

    Université d'Avignon, France
The $\varepsilon$-strategy in variational analysis: illustration with the closed convexification of a function cover
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Abstract

In this work, we concentrate our interest and efforts on general variational (or optimization) problems which do not have solutions necessarily, but which do have approximate solutions (or solutions within ε>0\varepsilon > 0). We shall see how to recover all the (exact) minimizers of the relaxed version of the original problem (by closed-convexification of the objective function) in terms of the ε\varepsilon -minimizers of the original problem. Applications to two approximation problems in a Hilbert space setting will be shown.

Cite this article

Jean-Baptiste Hiriart-Urruty, Marco A. López, Michel Volle, The ε\varepsilon-strategy in variational analysis: illustration with the closed convexification of a function. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 449–474

DOI 10.4171/RMI/643