Geodesic
Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space
Journal of convex analysis, Tome 27 (2020) no. 3, pp. 1033-1049
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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.
Classification : 47N10, 46N10, 46E15
Mots-clés : Isomorphism, minimization problem, convex functions, normal Hausdorff space, the Stone-Cech compactification 
@article{JCA_2020_27_3_JCA_2020_27_3_a14,
     author = {M. Bachir},
     title = {Convex {Extension} of {Lower} {Semicontinuous} {Functions} {Defined} on {Normal} {Hausdorff} {Space}},
     journal = {Journal of convex analysis},
     pages = {1033--1049},
     year = {2020},
     volume = {27},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a14/}
}
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M. Bachir. Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space. Journal of convex analysis, Tome 27 (2020) no. 3, pp. 1033-1049. http://geodesic.mathdoc.fr/item/JCA_2020_27_3_JCA_2020_27_3_a14/