scholarly journals Distributed algorithms for computing a fixed point of multi-agent nonexpansive operators

Automatica ◽  
2020 ◽  
Vol 122 ◽  
pp. 109286
Author(s):  
Xiuxian Li ◽  
Lihua Xie
Keyword(s):  
Fixed Point ◽  
Distributed Algorithms ◽  
Multi Agent ◽  
Nonexpansive Operators

scholarly journals A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 378 ◽  
Author(s):  
Adisak Hanjing ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Image Restoration ◽  
Optimization Method ◽  
Convergence Result ◽  
Fixed Point Algorithm ◽  
Convergence Behavior ◽  
Lower Semi ◽  
Restoration Algorithm ◽  
Nonexpansive Operators

In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. Using our main result, we obtain a new accelerated image restoration algorithm, called the forward-backward modified W-algorithm (FBMWA), for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply the FBMWA algorithm to solving image restoration problems. We analyze and compare convergence behavior of our method with the others for deblurring the image. We found that our algorithm has a higher efficiency than the others in the literature.

scholarly journals Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tongxin Xu ◽  
Luoyi Shi
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Nonexpansive Operators ◽  
Split Feasibility

AbstractIn this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent literature.

scholarly journals Solving Composite Fixed Point Problems with Block Updates

2021 ◽  
Vol 10 (1) ◽  
pp. 1154-1177
Author(s):  
Patrick L. Combettes ◽  
Lilian E. Glaudin
Keyword(s):  
Fixed Point ◽  
Nonsmooth Analysis ◽  
Data Science ◽  
Linear Convergence ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Monotone Inclusions ◽  
Minimization Problems ◽  
Convergence Results ◽  
Nonexpansive Operators

Abstract Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at each iteration, and the question of maintaining convergence while updating only blocks of operators is open. We propose a method that achieves this goal and analyze its asymptotic behavior. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays. Applications to several nonlinear and nonsmooth analysis problems are presented, ranging from monotone inclusions and inconsistent feasibility problems, to variational inequalities and minimization problems arising in data science.

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