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Article Dans Une Revue Revista Matemática Iberoamericana Année : 2011

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

Marco A. López
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Michel Volle
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Résumé

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). 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-minimizers of the original problem. Applications to two approximation problems in a Hilbert space setting will be shown.
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Dates et versions

hal-00995827 , version 1 (07-06-2023)

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Citer

Jean-Baptiste Hiriart-Urruty, Marco A. López, Michel Volle. The ε-strategy in variational analysis : illustration with the closed convexification of a function. Revista Matemática Iberoamericana, 2011, 27 (2), p. 449--474. ⟨10.4171/RMI/643⟩. ⟨hal-00995827⟩
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