Dual characterizations of relative continuity of convex functions

Authors
Benoist, J Daniilidis, A
Citation
J. Benoist et A. Daniilidis, Dual characterizations of relative continuity of convex functions, J AUS MAT A, 70, 2001, pp. 211-223
Citations number
8
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
70
Year of publication
2001
Part
2
Pages
211 - 223
Database
ISI
SICI code
0263-6115(200104)70:<211:DCORCO>2.0.ZU;2-E
Abstract
Various properties of continuity for the class of lower semicontinuous conv ex functions are considered and dual characterizations are established. In particular, it is shown that the restriction of a lower semicontinuous conv ex function to its domain (respectively, domain of subdifferentiability) is continuous if and only if its subdifferential is strongly cyclically monot one (respectively, sigma -cyclically monotone).