Journal of dynamics and differential equations, ISSN 1572-9222, 2015, Volume 29, Issue 1, pp. 155 - 168

We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak...

Lyapunov analysis | Krasnosel’skiĭ–Mann algorithm | Mathematics | Dynamical systems | 34G25 | Ordinary Differential Equations | Monotone inclusions | 90C25 | Applications of Mathematics | 47J25 | 47H05 | Partial Differential Equations | Forward–backward algorithm | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | Krasnosel'skii-Mann algorithm | SPLITTING ALGORITHM | CONVERGENCE | Forward-backward algorithm | Analysis | Algorithms

Lyapunov analysis | Krasnosel’skiĭ–Mann algorithm | Mathematics | Dynamical systems | 34G25 | Ordinary Differential Equations | Monotone inclusions | 90C25 | Applications of Mathematics | 47J25 | 47H05 | Partial Differential Equations | Forward–backward algorithm | MATHEMATICS | HILBERT-SPACES | MATHEMATICS, APPLIED | Krasnosel'skii-Mann algorithm | SPLITTING ALGORITHM | CONVERGENCE | Forward-backward algorithm | Analysis | Algorithms

Journal Article

Journal of global optimization, ISSN 1573-2916, 2018, Volume 73, Issue 4, pp. 801 - 824

In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ–Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces...

Nonexpansive operator | Monotone inclusion | Bounded perturbation resilience | Forward–backward splitting method | Mathematics | Optimization | Douglas–Rachford splitting method | Davis–Yin splitting method | Backward–forward splitting method | Operations Research/Decision Theory | Multi-step inertial Krasnosel’skiǐ–Mann algorithm | Computer Science, general | Real Functions | SUPERIORIZATION | MATHEMATICS, APPLIED | Forward-backward splitting method | Backward-forward splitting method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT METHODS | Multi-step inertial Krasnosel'skii-Mann algorithm | Douglas-Rachford splitting method | Davis-Yin splitting method | Splitting | Hilbert space | Algorithms | Iterative methods | Convergence

Nonexpansive operator | Monotone inclusion | Bounded perturbation resilience | Forward–backward splitting method | Mathematics | Optimization | Douglas–Rachford splitting method | Davis–Yin splitting method | Backward–forward splitting method | Operations Research/Decision Theory | Multi-step inertial Krasnosel’skiǐ–Mann algorithm | Computer Science, general | Real Functions | SUPERIORIZATION | MATHEMATICS, APPLIED | Forward-backward splitting method | Backward-forward splitting method | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | GRADIENT METHODS | Multi-step inertial Krasnosel'skii-Mann algorithm | Douglas-Rachford splitting method | Davis-Yin splitting method | Splitting | Hilbert space | Algorithms | Iterative methods | Convergence

Journal Article

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Proximal point algorithms for nonsmooth convex optimization with fixed point constraints

European journal of operational research, ISSN 0377-2217, 2016, Volume 253, Issue 2, pp. 503 - 513

....•We propose the Halpern-type incremental proximal algorithm for solving the problem.•We propose the Mann-type incremental proximal algorithm for solving the problem...

Proximal point algorithm | Krasnosel’skiĭ–Mann algorithm | Halpern algorithm | Fixed point | Incremental subgradient method | Krasnosel'ski -Mann algorithm | SPARSITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | SUBGRADIENT METHODS | Krasnosel'skit-Mann algorithm | Problem solving | Algorithms | Mathematical optimization | Analysis | Computational geometry | Fixed points (mathematics) | Mathematical analysis | Clusters | Hilbert space | Mathematical models | Convexity | Optimization

Proximal point algorithm | Krasnosel’skiĭ–Mann algorithm | Halpern algorithm | Fixed point | Incremental subgradient method | Krasnosel'ski -Mann algorithm | SPARSITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION | SUBGRADIENT METHODS | Krasnosel'skit-Mann algorithm | Problem solving | Algorithms | Mathematical optimization | Analysis | Computational geometry | Fixed points (mathematics) | Mathematical analysis | Clusters | Hilbert space | Mathematical models | Convexity | Optimization

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

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

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 32

This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search...

65K05 | Mathematical and Computational Biology | nonexpansive mapping | Mathematics | Topology | Krasnosel’skiĭ-Mann fixed point algorithm | constrained smooth convex optimization | 47H10 | 90C25 | Analysis | line search method | Mathematics, general | Applications of Mathematics | Differential Geometry | fixed point problem | nonlinear conjugate gradient methods | generalized convex feasibility problem | Computational geometry | Constraints | Algorithms | Searching | Conjugate gradients | Nonlinearity | Convexity | Optimization

65K05 | Mathematical and Computational Biology | nonexpansive mapping | Mathematics | Topology | Krasnosel’skiĭ-Mann fixed point algorithm | constrained smooth convex optimization | 47H10 | 90C25 | Analysis | line search method | Mathematics, general | Applications of Mathematics | Differential Geometry | fixed point problem | nonlinear conjugate gradient methods | generalized convex feasibility problem | Computational geometry | Constraints | Algorithms | Searching | Conjugate gradients | Nonlinearity | Convexity | Optimization

Journal Article

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Generalized Krasnoselskii–Mann-type iterations for nonexpansive mappings in Hilbert spaces

Computational optimization and applications, ISSN 1573-2894, 2017, Volume 67, Issue 3, pp. 595 - 620

The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is known to be weakly convergent in...

Weak convergence | Krasnoselskii–Mann iteration | Splitting methods | Strong convergence | Fermat–Weber problem | Alternating projection method | Hilbert spaces | Nonexpansive operators | Fermat-Weber problem | MATHEMATICS, APPLIED | APPROXIMATION | ALGORITHMS | FAMILY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEAK-CONVERGENCE | Krasnoselskii-Mann iteration | FIXED-POINTS | STRONG-CONVERGENCE | Optimization algorithms | Fixed points (mathematics) | Site selection | Convergence

Weak convergence | Krasnoselskii–Mann iteration | Splitting methods | Strong convergence | Fermat–Weber problem | Alternating projection method | Hilbert spaces | Nonexpansive operators | Fermat-Weber problem | MATHEMATICS, APPLIED | APPROXIMATION | ALGORITHMS | FAMILY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | WEAK-CONVERGENCE | Krasnoselskii-Mann iteration | FIXED-POINTS | STRONG-CONVERGENCE | Optimization algorithms | Fixed points (mathematics) | Site selection | Convergence

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

nonexpansive operators | fixed point | optimization | Distributed algorithms | Krasnosel'skii-Mann iteration | multi-agent networks

Journal Article

IEEE transactions on medical imaging, ISSN 1558-254X, 2019, Volume 38, Issue 9, pp. 2114 - 2126

This paper presents a preconditioned Krasnoselskii-Mann (KM) algorithm with an improved EM preconditioner (IEM-PKMA...

Krasnoselskii-Mann algorithm | TV | Convex functions | total variation | Positron emission tomography | maximum likelihood estimation | Image reconstruction | Optimization | Convergence | Biomedical imaging | TOMOGRAPHY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, BIOMEDICAL | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | image reconstruction | positron emission tomography | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | ENGINEERING, ELECTRICAL & ELECTRONIC | Brain - diagnostic imaging | Algorithms | Humans | Middle Aged | Male | Image Processing, Computer-Assisted - methods | Positron-Emission Tomography - methods | Phantoms, Imaging

Krasnoselskii-Mann algorithm | TV | Convex functions | total variation | Positron emission tomography | maximum likelihood estimation | Image reconstruction | Optimization | Convergence | Biomedical imaging | TOMOGRAPHY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, BIOMEDICAL | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | image reconstruction | positron emission tomography | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | ENGINEERING, ELECTRICAL & ELECTRONIC | Brain - diagnostic imaging | Algorithms | Humans | Middle Aged | Male | Image Processing, Computer-Assisted - methods | Positron-Emission Tomography - methods | Phantoms, Imaging

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, pp. 403 - 434

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skiĭ–Mann iteration built from non-expansive operators. The presented results...

Monotone inclusion | Theoretical, Mathematical and Computational Physics | Convergence rates | Non-expansive operator | Asymptotic regularity | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Krasnosel’skiĭ–Mann iteration | 47H09 | Combinatorics | 47H05 | MATHEMATICS, APPLIED | Krasnosel'skii-Mann iteration | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | WEAK-CONVERGENCE | CONVEX MINIMIZATION | Studies | Mathematical analysis | Asymptotic methods | Optimization | Convergence | Mathematical programming | Operators (mathematics) | Operators | Splitting | Approximation | Criteria | Iterative methods

Monotone inclusion | Theoretical, Mathematical and Computational Physics | Convergence rates | Non-expansive operator | Asymptotic regularity | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Krasnosel’skiĭ–Mann iteration | 47H09 | Combinatorics | 47H05 | MATHEMATICS, APPLIED | Krasnosel'skii-Mann iteration | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | WEAK-CONVERGENCE | CONVEX MINIMIZATION | Studies | Mathematical analysis | Asymptotic methods | Optimization | Convergence | Mathematical programming | Operators (mathematics) | Operators | Splitting | Approximation | Criteria | Iterative methods

Journal Article

Journal of fixed point theory and applications, ISSN 1661-7746, 2019, Volume 21, Issue 2, pp. 1 - 22

In this paper, we suggest two inertial Krasnosel’skiǐ–Mann type hybrid algorithms to approximate a solution of a hierarchical fixed point problem for nonexpansive mappings in Hilbert space...

49J35 | Mathematical Methods in Physics | inertial Krasnosel’skiǐ–Mann type hybrid algorithm | 47H10 | 90C47 | Analysis | Mathematics, general | Hierarchical fixed point problem | nonexpansive mapping | Mathematics | strong convergence | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | PROXIMAL METHOD | ITERATIVE METHOD | inertial Krasnosel'skii-Mann type hybrid algorithm | MATHEMATICS | THEOREMS | FORWARD-BACKWARD ALGORITHM | MONOTONE-OPERATORS | STRONG-CONVERGENCE

49J35 | Mathematical Methods in Physics | inertial Krasnosel’skiǐ–Mann type hybrid algorithm | 47H10 | 90C47 | Analysis | Mathematics, general | Hierarchical fixed point problem | nonexpansive mapping | Mathematics | strong convergence | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | PROXIMAL METHOD | ITERATIVE METHOD | inertial Krasnosel'skii-Mann type hybrid algorithm | MATHEMATICS | THEOREMS | FORWARD-BACKWARD ALGORITHM | MONOTONE-OPERATORS | STRONG-CONVERGENCE

Journal Article

Applied mathematics & optimization, ISSN 1432-0606, 2019, Volume 80, Issue 3, pp. 547 - 598

In a Hilbert space $${{\mathcal {H}}}$$ H , we study the convergence properties of a class of relaxed inertial forward–backward algorithms...

65K05 | Systems Theory, Control | Inertial Krasnoselskii–Mann iteration | Theoretical, Mathematical and Computational Physics | Mathematics | Relaxation | Mathematical Methods in Physics | Inertial forward–backward algorithms | Calculus of Variations and Optimal Control; Optimization | 90C25 | Nash equilibration | Structured monotone inclusions | Convergence rate | 65K10 | Numerical and Computational Physics, Simulation | 49M37 | Cocoercive operators

65K05 | Systems Theory, Control | Inertial Krasnoselskii–Mann iteration | Theoretical, Mathematical and Computational Physics | Mathematics | Relaxation | Mathematical Methods in Physics | Inertial forward–backward algorithms | Calculus of Variations and Optimal Control; Optimization | 90C25 | Nash equilibration | Structured monotone inclusions | Convergence rate | 65K10 | Numerical and Computational Physics, Simulation | 49M37 | Cocoercive operators

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

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

Optimization methods & software, ISSN 1029-4937, 2016, Volume 31, Issue 5, pp. 931 - 951

... of nonexpansive mappings in a real Hilbert space. The proposed algorithm can work in nonsmooth optimization over constraint sets onto which projections cannot be always implemented, whereas the conventional incremental subgradient method...

nonsmooth convex optimization | subdifferential | nonexpansive mapping | incremental subgradient method | fixed point | Krasnosel'skiĭ-Mann algorithm | Krasnosel'skiĭ–Mann algorithm | SPARSITY | MATHEMATICS, APPLIED | 65K05 | MAXIMAL MONOTONE-OPERATORS | DISTRIBUTED OPTIMIZATION | SIGNAL RECOVERY | SUM | ALGORITHMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Krasnosel'ski-Mann algorithm | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C25 | 90C90 | CONVERGENCE | DIVERSITY | SPLITTING METHOD | Queuing theory | Algorithms | Convex analysis | Optimization | Approximation | Mathematical analysis | Projection | Constants | Mathematical models | Convergence

nonsmooth convex optimization | subdifferential | nonexpansive mapping | incremental subgradient method | fixed point | Krasnosel'skiĭ-Mann algorithm | Krasnosel'skiĭ–Mann algorithm | SPARSITY | MATHEMATICS, APPLIED | 65K05 | MAXIMAL MONOTONE-OPERATORS | DISTRIBUTED OPTIMIZATION | SIGNAL RECOVERY | SUM | ALGORITHMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | Krasnosel'ski-Mann algorithm | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | 90C25 | 90C90 | CONVERGENCE | DIVERSITY | SPLITTING METHOD | Queuing theory | Algorithms | Convex analysis | Optimization | Approximation | Mathematical analysis | Projection | Constants | Mathematical models | Convergence

Journal Article

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Iterative algorithms for the multiple-sets split feasibility problem in Hilbert spaces

Numerical Algorithms, ISSN 1017-1398, 11/2017, Volume 76, Issue 3, pp. 783 - 798

.... We show that particular cases of our algorithms are some improvements for existing ones in literature...

Algorithms | Algebra | Variational inequality | 49J30 | Numerical Analysis | Computer Science | Numeric Computing | 47H09 | Theory of Computation | 47J05 | Nonexpansive mapping | Fixed point | VARIATIONAL-INEQUALITIES | KRASNOSELSKII-MANN ALGORITHM | MATHEMATICS, APPLIED | STEEPEST-DESCENT

Algorithms | Algebra | Variational inequality | 49J30 | Numerical Analysis | Computer Science | Numeric Computing | 47H09 | Theory of Computation | 47J05 | Nonexpansive mapping | Fixed point | VARIATIONAL-INEQUALITIES | KRASNOSELSKII-MANN ALGORITHM | MATHEMATICS, APPLIED | STEEPEST-DESCENT

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 17

Nonsmooth convex optimization problems are solved over fixed point sets of nonexpansive mappings by using a distributed optimization technique. This is done...

nonsmooth convex optimization | 65K05 | Mathematical and Computational Biology | parallel algorithm | subgradient | nonexpansive mapping | Mathematics | Topology | 90C25 | fixed point | Analysis | Mathematics, general | 90C90 | Applications of Mathematics | Differential Geometry | Krasnosel’skiĭ-Mann algorithm | MATHEMATICS | SUM | Krasnosel'ski. i-Mann algorithm | ALGORITHMS | SPLITTING METHOD | Fixed point theory | Usage | Mathematical optimization | Parallel computers | Mappings (Mathematics) | Computational geometry | Operators | Fixed points (mathematics) | Algorithms | Mathematical analysis | Mathematical models | Mapping | Convexity | Optimization

nonsmooth convex optimization | 65K05 | Mathematical and Computational Biology | parallel algorithm | subgradient | nonexpansive mapping | Mathematics | Topology | 90C25 | fixed point | Analysis | Mathematics, general | 90C90 | Applications of Mathematics | Differential Geometry | Krasnosel’skiĭ-Mann algorithm | MATHEMATICS | SUM | Krasnosel'ski. i-Mann algorithm | ALGORITHMS | SPLITTING METHOD | Fixed point theory | Usage | Mathematical optimization | Parallel computers | Mappings (Mathematics) | Computational geometry | Operators | Fixed points (mathematics) | Algorithms | Mathematical analysis | Mathematical models | Mapping | Convexity | Optimization

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

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

Mathematics (Basel), ISSN 2227-7390, 2019, Volume 7, Issue 2, p. 131

The resolvent is a fundamental concept in studying various operator splitting algorithms...

Krasnoselskii-Mann algorithm | Resolvent | Yoshida approximation | Douglas-Rachford splitting algorithm | Maximally monotone operators | maximally monotone operators | MATHEMATICS | MONOTONE | resolvent | CONVEX MINIMIZATION | POINT ALGORITHM | Krasnoselskii–Mann algorithm | Douglas–Rachford splitting algorithm

Krasnoselskii-Mann algorithm | Resolvent | Yoshida approximation | Douglas-Rachford splitting algorithm | Maximally monotone operators | maximally monotone operators | MATHEMATICS | MONOTONE | resolvent | CONVEX MINIMIZATION | POINT ALGORITHM | Krasnoselskii–Mann algorithm | Douglas–Rachford splitting algorithm

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 382, Issue 2, pp. 631 - 644

In this paper, we present iteration schemes to weakly and strongly approximate common fixed points of a finite family of a class of strict pseudocontractions.

Krasnoselskii–Mann iteration | Strict pseudocontractions | Cyclic algorithms | q-Uniformly smooth Banach spaces | Common fixed points | Convergence | Krasnoselskii-Mann iteration | Q-Uniformly smooth Banach spaces | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FINITE FAMILY | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | MATHEMATICS | BROWDER-PETRYSHYN TYPE | SMOOTH BANACH-SPACES | PSEUDO-CONTRACTIONS | OPTIMIZATION | Algorithms

Krasnoselskii–Mann iteration | Strict pseudocontractions | Cyclic algorithms | q-Uniformly smooth Banach spaces | Common fixed points | Convergence | Krasnoselskii-Mann iteration | Q-Uniformly smooth Banach spaces | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FINITE FAMILY | ACCRETIVE-OPERATORS | STRONG-CONVERGENCE THEOREMS | MONOTONE MAPPINGS | MATHEMATICS | BROWDER-PETRYSHYN TYPE | SMOOTH BANACH-SPACES | PSEUDO-CONTRACTIONS | OPTIMIZATION | Algorithms

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

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

Nonlinear Analysis, ISSN 0362-546X, 2010, Volume 72, Issue 2, pp. 704 - 709

We consider a variable Krasnosel’skii–Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping p r o x λ f...

Krasnosel’skii–Mann algorithm | Fixed-point | Optimization | Prox-regularity | Krasnosel'skii-Mann algorithm | MATHEMATICS | MATHEMATICS, APPLIED | SET | ALGORITHM | REGULAR FUNCTIONS | CONVERGENCE | Fighter planes | Mathematical optimization | Algorithms | Approximation | Equivalence | Nonlinearity | Mapping | Iterative methods | Regularity | Mathematics | Optimization and Control

Krasnosel’skii–Mann algorithm | Fixed-point | Optimization | Prox-regularity | Krasnosel'skii-Mann algorithm | MATHEMATICS | MATHEMATICS, APPLIED | SET | ALGORITHM | REGULAR FUNCTIONS | CONVERGENCE | Fighter planes | Mathematical optimization | Algorithms | Approximation | Equivalence | Nonlinearity | Mapping | Iterative methods | Regularity | Mathematics | Optimization and Control

Journal Article