A 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 * 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.

Keywords: Isomorphism; minimization problem; convex functions; normal Hausdorff space; the Stone-Čech compactification; Msc: 47N10; 46N10; 46E15

Domains: Functional Analysis [math.FA]

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