Randomized sparse block Kaczmarz as randomized dual block-coordinate descent
- We show that the Sparse Kaczmarz method is a particular instanceof the coordinate gradient method applied to an unconstrained dualproblem corresponding to a regularized `1-minimization problem sub-ject to linear constraints. Based on this observation and recent the-oretical work concerning the convergence analysis and correspondingconvergence rates for the randomized block coordinate gradient descentmethod, we derive block versions and consider randomized ordering ofblocks of equations. Convergence in expectation is thus obtained as abyproduct. By smoothing the `1-objective we obtain a strongly convexdual which opens the way to various acceleration schemes.
| Author: | Stefania PetraORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1106919 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/110691 |
| ISSN: | 1844-0835OPAC |
| Parent Title (Romanian): | Analele Universitatii "Ovidius" Constanta - Seria Matematica |
| Publisher: | Walter de Gruyter |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2015 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/01/08 |
| Volume: | 23 |
| Issue: | 3 |
| First Page: | 129 |
| Last Page: | 149 |
| DOI: | https://doi.org/10.1515/auom-2015-0052 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Mathematische Bildverarbeitung | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung |
