The unique minimal dual representation of a convex function


Journal Article

Suppose (i) X is a separable Banach space, (ii) C is a convex subset of X that is a Baire space (when endowed with the relative topology) such that aff(C) is dense in X, and (iii) f:C→R is locally Lipschitz continuous and convex. The Fenchel-Moreau duality can be stated asf(x)=maxx*∈M[〈x,x*〉-f*(x*)], for all x∈C, where f* denotes the Fenchel conjugate of f and M=X*. We show that, under assumptions (i)-(iii), there is a unique minimal weak*-closed subset Mf of X* for which the above duality holds. © 2010 Elsevier Inc.

Full Text

Duke Authors

Cited Authors

  • Ergin, H; Sarver, T

Published Date

  • October 1, 2010

Published In

Volume / Issue

  • 370 / 2

Start / End Page

  • 600 - 606

Electronic International Standard Serial Number (EISSN)

  • 1096-0813

International Standard Serial Number (ISSN)

  • 0022-247X

Digital Object Identifier (DOI)

  • 10.1016/j.jmaa.2010.04.017

Citation Source

  • Scopus