Applications of accelerated computational methods for quasi-nonexpansive operators to optimization problems

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...

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Bibliographic Details
Published in:Soft computing (Berlin, Germany) Vol. 24; no. 23; pp. 17887 - 17911
Main Author: Sahu, D. R.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Codes
Computational Intelligence
Control
Convergence
Convexity
Engineering
Feasibility
Fixed points (mathematics)
Hilbert space
Iterative methods
Mathematical Logic and Foundations
Mechatronics
Methodologies and Application
Methods
Numerical methods
Operators
Optimization
Robotics
S-iteration method
Convex optimization
Lasso problem
Fixed-point set
Maximal monotone operator
Nonexpansive
Fixed-point algorithm
Proximal gradient method
ISSN:1432-7643, 1433-7479
Online Access:Get full text
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Summary: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.
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-020-05038-9