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-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.

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Keywords

  • Isomorphism
  • minimization problem
  • convex functions
  • normal Hausdorff space
  • the Stone-Čech compactification

Mathematics Subject Classification

47N10, 46N10, 46E15

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Suggested citation

M. Bachir. “Convex Extension of Lower Semicontinuous Functions Defined on Normal Hausdorff Space.” Journal of Convex Analysis 27 (2020), No. 3, 1033–1049. https://doi.org/10.68381/jca27054

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.