Back to Search
Start Over
Conical averagedness and convergence analysis of fixed point algorithms.
- Source :
- Journal of Global Optimization; Feb2022, Vol. 82 Issue 2, p351-373, 23p
- Publication Year :
- 2022
-
Abstract
- We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward–backward algorithm, and the adaptive Douglas–Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics. [ABSTRACT FROM AUTHOR]
- Subjects :
- FORWARD-backward algorithm
MONOTONE operators
RESOLVENTS (Mathematics)
ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 09255001
- Volume :
- 82
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Global Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 155024363
- Full Text :
- https://doi.org/10.1007/s10898-021-01057-4