The $\varepsilon$-strategy in variational analysis: illustration with the closed convexification of a function
Jean-Baptiste
Hiriart-Urruty
,
Marco A.
López
, and
Michel
Volle
Source: Rev. Mat. Iberoamericana Volume 27, Number 2
(2011), 449-474.
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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Keywords: $\varepsilon$-solutions in variational problems; relaxation; closed-convexification; approximate projections
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Zentralblatt MATH identifier: 05936698
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