Abstract
Of central importance in convex analysis are conditions guaranteeing that the conjugate of a sum is the infimal convolution of the conjugates. The main result in this direction is a theorem due to Attouch and Brézis. In turn, it gives rise to the Fenchel–Rockafellar duality framework for convex optimization problems.
This is a preview of subscription content, log in via an institution to check access.
References
_________ , Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Bauschke, H.H., Combettes, P.L. (2017). Fenchel–Rockafellar Duality. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-48311-5_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-48311-5_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-48310-8
Online ISBN: 978-3-319-48311-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)