Journal of Convex Analysis 27 (2020), No. 3, 1033--1049
Copyright Heldermann Verlag 2020
Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space
Laboratoire SAMM 4543, Université Panth\'eon-Sorbonne, 75634 Paris 13, France
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-star lower semicontinuous convex function defined on a weak-star convex compact subset of some dual Banach space. We establish the existence of a bijective operator between the two classes of functions which preserves problems of minimization.
Keywords: Isomorphism, minimization problem, convex functions, normal Hausdorff space, the Stone-Cech compactification.
MSC: 47N10, 46N10, 46E15.
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