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VARIOUS NOTIONS OF NONEXPANSIVENESS COINCIDE FOR PROXIMAL MAPPINGS OF FUNCTIONS.
- Source :
-
SIAM Journal on Optimization . 2024, Vol. 34 Issue 1, p642-653. 12p. - Publication Year :
- 2024
-
Abstract
- Proximal mappings are essential in splitting algorithms for both convex and noncon-vex optimization. In this paper, we show that proximal mappings of every prox-bounded function are nonexpansive if and only if they are firmly nonexpansive if and only if they are averaged if and only if the function is convex. Lipschitz proximal mappings of prox-bounded functions are also characterized via hypoconvex or strongly convex functions. Our results generalize a recent result due to Rockafellar [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONEXPANSIVE mappings
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 10526234
- Volume :
- 34
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 176824674
- Full Text :
- https://doi.org/10.1137/23M1597009