## 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
- 4904 Pure mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

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.2010.04.017Ergin, 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.

## 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
- 4904 Pure mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0906 Electrical and Electronic Engineering
- 0102 Applied Mathematics
- 0101 Pure Mathematics