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Applications of accelerated computational methods for quasi-nonexpansive operators to optimization problems.
- Source :
-
Soft Computing - A Fusion of Foundations, Methodologies & Applications . Dec2020, Vol. 24 Issue 23, p17887-17911. 25p. - Publication Year :
- 2020
-
Abstract
- This paper studies the convergence rates of two accelerated computational methods without assuming nonexpansivity of the underlying operators with convex and affine domains in infinite-dimensional Hilbert spaces. One method is a noninertial method, and its convergence rate is estimated as R T , { x n } (n) = o 1 n in worst case. The other is an inertial method, and its convergence rate is estimated as R T , { y n } (n) = o 1 n under practical conditions. Then, we apply our results to give new results on convergence rates for solving generalized split common fixed-point problems for the class of demimetric operators. We also apply our results to variational inclusion problems and convex optimization problems. Our results significantly improve and/or develop previously discussed fixed-point problems and splitting problems and related algorithms. To demonstrate the applicability of our methods, we provide numerical examples for comparisons and numerical experiments on regression problems for publicly available high-dimensional real datasets taken from different application domains. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CONVEX domains
*HILBERT space
*MONOTONE operators
Subjects
Details
- Language :
- English
- ISSN :
- 14327643
- Volume :
- 24
- Issue :
- 23
- Database :
- Academic Search Index
- Journal :
- Soft Computing - A Fusion of Foundations, Methodologies & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 146975859
- Full Text :
- https://doi.org/10.1007/s00500-020-05038-9