scholarly journals Globally Convergent Type-I Anderson Acceleration for Nonsmooth Fixed-Point Iterations

2020 ◽  
Vol 30 (4) ◽  
pp. 3170-3197
Author(s):  
Junzi Zhang ◽  
Brendan O'Donoghue ◽  
Stephen Boyd
Keyword(s):  
Fixed Point ◽  
Type I ◽  
Globally Convergent ◽  
Anderson Acceleration ◽  
Fixed Point Iterations

scholarly journals Anderson Acceleration for Fixed-Point Iterations

2011 ◽  
Vol 49 (4) ◽  
pp. 1715-1735 ◽  
Author(s):  
Homer F. Walker ◽  
Peng Ni
Keyword(s):  
Fixed Point ◽  
Anderson Acceleration ◽  
Fixed Point Iterations

A Note on "Implicit Mann Fixed Point Iterations for Pseudo-Contractive Mappings"

2011 ◽  
Vol 393-395 ◽  
pp. 543-545
Author(s):  
Hong Jun Li ◽  
Yong Fu Su
Keyword(s):  
Fixed Point ◽  
Convergence Theorem ◽  
Nonempty Subset ◽  
Applied Mathematics ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Contractive Mappings ◽  
Contractive Map ◽  
Fixed Point Iterations ◽  
Implicit Iteration

Ljubomir Ciric, Arif Rafiq, Nenad Cakic, Jeong Sheok Umed [ Implicit Mann fixed point iterations for pseudo-contractive mappings, Applied Mathematics Letters 22 (2009) 581-584] introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the relatively convergence theorem. However, the content of mann theorem is fuzzy. In this paper, we will give some comments . Let be a Banach space and be a nonempty subset of . A mapping is called hemi-contractive (see [1]) if and In [1], the authors introduced and investigated a modified Mann implicit iteration process for continuous hemi-contractive map. They proved the following convergence theorem.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals New Double Projection Algorithm for Solving Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lian Zheng
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Projection Algorithm ◽  
Iterative Sequence ◽  
Local Error ◽  
Projection Algorithms ◽  
Local Error Bound ◽  
Globally Convergent

We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient.

scholarly journals On analytical and numerical study of implicit fixed point iterations

2015 ◽  
Vol 2 (1) ◽  
pp. 1021623
Author(s):  
Renu Chugh ◽  
Preety Malik ◽  
Vivek Kumar
Keyword(s):  
Fixed Point ◽  
Numerical Study ◽  
Fixed Point Iterations
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