Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space

Mohammed Bachir (1)

1 Equations d'evolution

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.

Domains: Functional Analysis [math.FA]

Mohammed Bachir. Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space. Journal of Convex Analysis, 2020, 27 (3). ⟨hal-02455711⟩