Fast Krasnosel’skiĭ–Mann Algorithm with a Convergence Rate of the Fixed Point Iteration of \(\boldsymbol{{ o} \left(\frac{1}{{ k}} \right)}\)
DOI10.1137/22m1504305arXiv2206.09462MaRDI QIDQ6091103
Dang-Khoa Nguyen, Radu Ioan Boţ
Publication date: 24 November 2023
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2206.09462
convergence ratesLyapunov analysisnonexpansive operatorKrasnosel'skiĭ-Mann iterationaveraged operatorconvergence of iteratesNesterov's momentum
Variational and other types of inequalities involving nonlinear operators (general) (47J20) Monotone operators and generalizations (47H05) Complexity and performance of numerical algorithms (65Y20) Numerical methods for variational inequalities and related problems (65K15)
Cites Work
- Unnamed Item
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- Convergence rates with inexact non-expansive operators
- Fast convex optimization via inertial dynamics with Hessian driven damping
- A dynamical system associated with the fixed points set of a nonexpansive operator
- A three-operator splitting scheme and its optimization applications
- On the convergence rate of Douglas-Rachford operator splitting method
- On the convergence rate of the Halpern-iteration
- Weak convergence theorems for nonexpansive mappings in Banach spaces
- Approximation of fixed points of nonexpansive mappings
- Sharp convergence rates for averaged nonexpansive maps
- On the rate of convergence of Krasnosel'skiĭ-Mann iterations and their connection with sums of Bernoullis
- A strongly convergent Krasnosel'skiǐ-Mann-type algorithm for finding a common fixed point of a countably infinite family of nonexpansive operators in Hilbert spaces
- Tight coefficients of averaged operators via scaled relative graph
- Accelerated proximal point method for maximally monotone operators
- A note on segmenting Mann iterates
- Convergence Rate Analysis of the Forward-Douglas-Rachford Splitting Scheme
- Iterative Algorithms for Nonlinear Operators
- Krasnoselski-Mann Iterations in Normed Spaces
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- Tight Sublinear Convergence Rate of the Proximal Point Algorithm for Maximal Monotone Inclusion Problems
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
- Shanks Sequence Transformations and Anderson Acceleration
- Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces
- ON THE CONVERGENCE RATE OF THE KRASNOSEL’SKIĬ–MANN ITERATION
- Convergence of Halpern’s Iteration Method with Applications in Optimization
- Convergence Rate Analysis of Several Splitting Schemes
- The solution by iteration of nonlinear functional equations in Banach spaces
- Fixed points of nonexpanding maps
- Weak convergence of the sequence of successive approximations for nonexpansive mappings
- A First Order Method for Solving Convex Bilevel Optimization Problems
- Mean Value Methods in Iteration
- Convex analysis and monotone operator theory in Hilbert spaces
- Optimal error bounds for non-expansive fixed-point iterations in normed spaces
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