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A convex extension of lower semicontinuous functions defined on normal Hausdorff space

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Mohammed Bachir
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Abstract

We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined on a weak * convex compact subset of some dual Banach space. We estalish the existence of an bijective operator between the two classes of functions which preserves the problems of minimization.
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hal-01525475 , version 1 (20-05-2017)

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Mohammed Bachir. A convex extension of lower semicontinuous functions defined on normal Hausdorff space. 2017. ⟨hal-01525475⟩
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