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May, 2011 The $\varepsilon$-strategy in variational analysis: illustration with the closed convexification of a function
Jean-Baptiste Hiriart-Urruty , Marco A. López , Michel Volle
Rev. Mat. Iberoamericana 27(2): 449-474 (May, 2011).

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 $\varepsilon > 0$). 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 $\varepsilon $-minimizers of the original problem. Applications to two approximation problems in a Hilbert space setting will be shown.

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Jean-Baptiste Hiriart-Urruty . Marco A. López . Michel Volle . "The $\varepsilon$-strategy in variational analysis: illustration with the closed convexification of a function." Rev. Mat. Iberoamericana 27 (2) 449 - 474, May, 2011.

Information

Published: May, 2011
First available in Project Euclid: 10 June 2011

zbMATH: 1229.90265
MathSciNet: MR2848527

Subjects:
Primary: 90C46, 90C48
Secondary: 49N15, 90C25

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.27 • No. 2 • May, 2011
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