Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-27T17:11:32.383Z Has data issue: false hasContentIssue false
  • English
  • Français

Degree of pointedness of a convex function

Published online by Cambridge University Press:  17 April 2009

Alberto Seeger
Alberto Seeger
Affiliation:
King Fahd University of Petroleum and Minerals, Department of Mathematical SciencesDhahran 31261Saudi Arabia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A convex function f is said to be pointed if its epigraph has a recession cone which is pointed. Partial pointedness of f refers to the case in which such a recession cone is only partially pointed. In this note we show that the degree of pointedness of f is related to the “thickness” of the effective domain of the conjugate function f*.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 159 - 167
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Benoist, J. and Hiriart-Urruty, J.B., ‘Quel est le sous-différentiel de l'enveloppe convexe fermée d'une fonction’, C.R. Acad. Sci. Paris. Sér. I 316 (1993), 233–237.Google Scholar
[2]Laurent, P.J., Approximation et optimisation (Hermann, Paris, 1972).Google Scholar
[3]Rockafellar, R.T., Convex analysis (Princeton University Press, Princeton, 1970).CrossRefGoogle Scholar
[4]Singer, I., ‘A Fenchel-Rockafellar type duality theorem for maximization’, Bull. Austral. Math. Soc. 29 (1979), 193–198.CrossRefGoogle Scholar
[5]Toland, J., ‘A duality principle for nonconvex optimization and the calculus of variations’, Arch. Rational Mech. Anal. 71 (1979), 41–61.Google Scholar