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Journal of dynamics and differential equations, ISSN 1572-9222, 2015, Volume 29, Issue 1, pp. 155 - 168
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 04/2015, Volume 256, pp. 472 - 487
We propose an inertial Douglas–Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties... 
Douglas–Rachford splitting | Krasnosel’skiı̆–Mann algorithm | Convex optimization | Primal–dual algorithm | Inertial splitting algorithm | Krasnosel'skiѣ-Mann algorithm Primal-dual algorithm Convex optimization | Douglas-Rachford splitting | MATHEMATICS, APPLIED | Primal-dual algorithm | Krasnosel'skii-Mann algorithm | MINIMIZATION | WEAK-CONVERGENCE | PROXIMAL POINT ALGORITHM | OPERATORS | COMPOSITE
Journal Article
IEEE transactions on automatic control, ISSN 0018-9286, 6/2020, pp. 1 - 1
.... To handle this problem, inspired by the centralized inexact Krasnosel'skii-Mann (IKM) iteration, we propose a distributed algorithm, called distributed inexact averaged operator algorithm (D-IAO... 
nonexpansive operators | fixed point | optimization | Distributed algorithms | Krasnosel'skii-Mann iteration | multi-agent networks
Journal Article
European journal of operational research, ISSN 0377-2217, 2016, Volume 253, Issue 2, pp. 503 - 513
Journal Article
Journal of fixed point theory and applications, ISSN 1661-7746, 2019, Volume 21, Issue 2, pp. 1 - 22
Journal Article
Carpathian Journal of Mathematics, ISSN 1584-2851, 1/2019, Volume 35, Issue 3, pp. 365 - 370
We prove that a cyclic coordinate fixed point algorithm for nonexpansive mappings when the underlying Hilbert space is decomposed into a Cartesian product of finitely many block spaces is weakly... 
Integers | Series convergence | Hilbert spaces | Coordinate systems | Real numbers | Dedicated to Prof. Qamrul Hasan Ansari on the occasion of his 60th anniversary | maximal monotone operator | MATHEMATICS | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | fixed point algorithm | Krasnoselskii-Mann | WEAK-CONVERGENCE | nonexpansive mapping | cyclic coordinate-update
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2017, Volume 96, Issue 1, pp. 162 - 170
.... Then we apply the result to give new results on convergence rates for the proximal point algorithm and the Douglas–Rachford method. 
Douglas-Rachford method | convergence rate | proximal point algorithm | Krasnosel'skiǐ-Mann iteration | nonexpansive | MATHEMATICS | MAXIMAL MONOTONE-OPERATORS | SPACES | Krasnosel'skii-Mann iteration | THEOREMS | WEAK-CONVERGENCE | SPLITTING METHOD
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2017, Volume 111, Issue 1, pp. 159 - 165
...–Mann algorithm $$x_{n+1}=\alpha _{n}x_{n}+(1-\alpha _{n})Tx_{n},$$ x n + 1 = α n x n + ( 1 - α n ) T x n , where $$\alpha _{n+1}=\max \{\alpha _{n},v(x_{n+1})\}.$$ α n + 1 = max { α n , v ( x n + 1 ) } . So, here the coefficients... 
Krasnoselskii-Mann algorithm | 47H10 | Non-self mappings | Strict pseudocontractions | Theoretical, Mathematical and Computational Physics | 47H09 | Mathematics, general | Fixed points | Mathematics | Applications of Mathematics | WEAK | MATHEMATICS | MAPPINGS | STRONG-CONVERGENCE THEOREMS | Construction | Algorithms | Approximation | Mathematical analysis | Texts | Hilbert space | Mapping | Convergence
Journal Article
Numerical Algorithms, ISSN 1017-1398, 11/2017, Volume 76, Issue 3, pp. 783 - 798
Journal Article
Mathematics (Basel), ISSN 2227-7390, 2019, Volume 7, Issue 2, p. 131
Journal Article
MATHEMATICS, ISSN 2227-7390, 04/2020, Volume 8, Issue 4, p. 638
In this paper, we give a general inertial Krasnoselskii-Mann algorithm for solving inclusion problems in Banach Spaces... 
q-uniformly smooth | NONEXPANSIVE-MAPPINGS | Krasnoselskii-Mann | PROXIMAL METHOD | ALGORITHM | nonexpansive mapping | SUM | Banach spaces | MATHEMATICS | CONVERGENCE THEOREMS | SHRINKAGE | forward-backward splitting method | MONOTONE-OPERATORS | FIXED-POINTS | Krasnoselskii–Mann
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 382, Issue 2, pp. 631 - 644
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2015, Volume 22, Issue 4, pp. 963 - 967
The Baillon-Haddad Theorem asserts that, if the gradient operator of a convex and Frechet differentiable function on a Hilbert space is nonexpansive, then it... 
Gradient | Baillon-Haddad Theorem | Krasnosel'skii-Mann Theorem | Firmly nonexpansive | Convex function | Nonexpansive | Bregman distance | MATHEMATICS | gradient | convex function | firmly nonexpansive | ALGORITHMS | nonexpansive
Journal Article
Optimization methods & software, ISSN 1029-4937, 2016, Volume 31, Issue 5, pp. 931 - 951
Journal Article
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