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The unique minimal dual representation of a convex function

Publication ,  Journal Article
Ergin, H; Sarver, T
Published in: Journal of Mathematical Analysis and Applications
October 1, 2010

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.

Duke Scholars

Published In

Journal of Mathematical Analysis and Applications

DOI

EISSN

1096-0813

ISSN

0022-247X

Publication Date

October 1, 2010

Volume

370

Issue

2

Start / End Page

600 / 606

Related Subject Headings

  • General Mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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ICMJE
MLA
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Ergin, H., & Sarver, T. (2010). The unique minimal dual representation of a convex function. Journal of Mathematical Analysis and Applications, 370(2), 600–606. https://doi.org/10.1016/j.jmaa.2010.04.017
Ergin, H., and T. Sarver. “The unique minimal dual representation of a convex function.” Journal of Mathematical Analysis and Applications 370, no. 2 (October 1, 2010): 600–606. https://doi.org/10.1016/j.jmaa.2010.04.017.
Ergin H, Sarver T. The unique minimal dual representation of a convex function. Journal of Mathematical Analysis and Applications. 2010 Oct 1;370(2):600–6.
Ergin, H., and T. Sarver. “The unique minimal dual representation of a convex function.” Journal of Mathematical Analysis and Applications, vol. 370, no. 2, Oct. 2010, pp. 600–06. Scopus, doi:10.1016/j.jmaa.2010.04.017.
Ergin H, Sarver T. The unique minimal dual representation of a convex function. Journal of Mathematical Analysis and Applications. 2010 Oct 1;370(2):600–606.
Journal cover image

Published In

Journal of Mathematical Analysis and Applications

DOI

EISSN

1096-0813

ISSN

0022-247X

Publication Date

October 1, 2010

Volume

370

Issue

2

Start / End Page

600 / 606

Related Subject Headings

  • General Mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics