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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Vydáno v:	Soft computing (Berlin, Germany) Ročník 24; číslo 23; s. 17887 - 17911
Hlavní autor:	Sahu, D. R.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2020 Springer Nature B.V
Témata:	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
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1432-7643 1433-7479
DOI:	10.1007/s00500-020-05038-9