- Title
- Conical averagedness and convergence analysis of fixed point algorithms
- Creator
- Bartz, Sedi; Dao, Minh; Phan, Hung
- Date
- 2022
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/184764
- Identifier
- vital:16563
- Identifier
-
https://doi.org/10.1007/s10898-021-01057-4
- Identifier
- ISBN:0925-5001 (ISSN)
- 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. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Publisher
- Springer
- Relation
- Journal of Global Optimization Vol. 82, no. 2 (2022), p. 351-373
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021, The Author(s)
- Rights
- Open Access
- Subject
- 4602 Artificial intelligence; 4901 Applied mathematics; 4903 Numerical and computational mathematics; Adaptive Douglas–Rachford algorithm; Cocoercivity; Conically averaged operator; Forward–backward algorithm; Proximal point algorithm; Strong monotonicity; Weak monotonicity
- Full Text
- Reviewed
- Funder
- SB was partially supported by a UMass Lowell faculty startup grant. MND was partially supported by Discovery Projects 160101537 and 190100555 from the Australian Research Council. HMP was partially supported by Autodesk, Inc. via a gift made to the Department of Mathematical Sciences, UMass Lowell.
- Hits: 1082
- Visitors: 1038
- Downloads: 78
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Accepted version | 339 KB | Adobe Acrobat PDF | View Details Download |