Self-Dual Smooth Approximations of Convex Functions via the Proximal Average

Heinz H. Bauschke (), Sarah M. Moffat and Xianfu Wang
Additional contact information
Heinz H. Bauschke: University of British Columbia

Chapter Chapter 2 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 23-32 from Springer

Abstract: Abstract The proximal average of two convex functions has proven to be a useful tool in convex analysis. In this note, we express the Goebel self-dual smoothing operator in terms of the proximal average, which allows us to give a different proof of self duality. We also provide a novel self-dual smoothing operator. Both operators are illustrated by smoothing the norm.

Keywords: Approximation; Convex function; Fenchel conjugate; Goebel smoothing operator; Moreau envelope; Proximal average (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations: View citations in EconPapers (1)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9569-8_2

Ordering information: This item can be ordered from
http://www.springer.com/9781441995698

DOI: 10.1007/978-1-4419-9569-8_2

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().