Journal ArticleDOI
A new method for split common fixed-point problem without priori knowledge of operator norms
TLDR
In this article, a new algorithm for the split common fixed-point problem is proposed, which does not need any priori information of the operator norm and establishes a weak convergence theorem.Abstract:
The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a linear transformation belongs to another fixed-point set. In this paper, we propose a new algorithm for the split common fixed-point problem that does not need any priori information of the operator norm. Under standard assumptions, we establish a weak convergence theorem of the proposed algorithm.read more
Citations
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Journal ArticleDOI
A new self-adaptive CQ algorithm with an application to the LASSO problem
Pham Ky Anh,Vu Tien Dung +1 more
TL;DR: A new self-adaptive CQ algorithm for solving split feasibility problems in real Hilbert spaces, designed, such that the stepsizes are directly computed at each iteration.
Journal ArticleDOI
A self-adaptive iterative algorithm for the split common fixed point problems
Jing Zhao,Dingfang Hou +1 more
TL;DR: The dual variable is used to propose a self-adaptive iterative algorithm for solving the split common fixed point problems of averaged mappings in real Hilbert spaces and gets the weak convergence of the proposed algorithm.
Journal ArticleDOI
The ball-relaxed CQ algorithms for the split feasibility problem
Hai Yu,Wanrong Zhan,Fenghui Wang +2 more
TL;DR: In this paper, a ball-relaxed projection method for the split feasibility problem is proposed, which replaces C and Q in the proposed algorithm by two properly chosen closed balls and.
Journal ArticleDOI
Iterative methods for the split feasibility problem and the fixed point problem in Banach spaces
TL;DR: In this paper, modifications of the self-adaptive method for solving the split feasibility problem and the fixed point problem of nonexpansive mappings in the framework of Banach spaces are proposed.
Journal ArticleDOI
Iterative solutions of the split common fixed point problem for strictly pseudo-contractive mappings
Huanhuan Cui,Luchuan Ceng +1 more
TL;DR: In this paper, the authors study the split common fixed point problem in Hilbert spaces and establish a weak convergence theorem for the method recently introduced by Wang, which extends a existing result from firmly nonexpansive mappings to strictly pseudo-contractive mapping.
References
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Book
Convex Analysis and Monotone Operator Theory in Hilbert Spaces
TL;DR: This book provides a largely self-contained account of the main results of convex analysis and optimization in Hilbert space, and a concise exposition of related constructive fixed point theory that allows for a wide range of algorithms to construct solutions to problems in optimization, equilibrium theory, monotone inclusions, variational inequalities, and convex feasibility.
Book
Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings
Kazimierz Goebel,Simeon Reich +1 more
Journal ArticleDOI
A unified treatment of some iterative algorithms in signal processing and image reconstruction
TL;DR: The Krasnoselskii?Mann (KM) approach to finding fixed points of nonlinear continuous operators on a Hilbert space was introduced in this article, where a wide variety of iterative procedures used in signal processing and image reconstruction and elsewhere are special cases of the KM iterative procedure.
Journal ArticleDOI
A multiprojection algorithm using Bregman projections in a product space
Yair Censor,Tommy Elfving +1 more
TL;DR: Using an extension of Pierra's product space formalism, it is shown here that a multiprojection algorithm converges and is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem.
Journal ArticleDOI
Iterative oblique projection onto convex sets and the split feasibility problem
TL;DR: In this article, the authors proposed a block-iterative version of the split feasibility problem (SFP) called the CQ algorithm, which involves only the orthogonal projections onto C and Q, which we shall assume are easily calculated, and involves no matrix inverses.
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A multiprojection algorithm using Bregman projections in a product space
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