Composite projection algorithms for the split feasibility problem

Yao, Yonghong; Yang, Pei-Xia; Kang, Shin Min

doi:10.1016/j.mcm.2012.07.026

Cited by 7 publications

(4 citation statements)

References 35 publications

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“…It is well-known that split feasibility problem (in short, SFP) is a model of several problems, namely, sensor network, radiation therapy treatment planning, resolution enhancement, wavelet-based denoising, antenna design, computerized tomography, materials sciences, watermarking, data compression, magnetic resonance imaging, color imaging, optics and neural networks, graph matching, adaptive filtering, image recovery; See, for example, [1,7,11,12,15] and the references therein. During the last decade, a large number of algorithms have been proposed for solving SFP under the nonemptyness of the solution set of SFP; See, for example, [1,7,[9][10][11][12]15,26,33,34,36] and references therein.…”

Section: Application To Split Feasibility Problemsmentioning

confidence: 99%

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

et al. 2016

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By using auxiliary principle technique, a new proximal point algorithm based on decomposition method is suggested for computing a weakly efficient solution of the constrained multiobjective optimization problem (MOP) without assuming the nonemptiness of its solution set. The optimality conditions for (MOP) are derived by the Lagrangian function of its subproblem and corresponding mixed variational inequality. Some basic properties and convergence results of the proposed method are established under some mild assumptions. As an application, we employ the proposed method to solve a split feasibility problem. Finally, numerical results are also presented to illustrate the feasibility of the proposed algorithm.

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Section: Application To Split Feasibility Problemsmentioning

confidence: 99%

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

et al. 2016

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“…where F(U) and F(T) mean the fixed point sets. If U and T are both metric projects, problem (1) is actually problem (2) [13,14], and further development of this topic made by [15][16][17][18][19]. To be more specific, given two nonempty closed convex sets C ⊂ H 1 and Q ⊂ H 2 and A is above mentioned.…”

Section: Introductionmentioning

confidence: 99%

Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

2019

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Two iterative algorithms are suggested for approximating a solution of the split common fixed point problem involved in pseudo-contractive operators without Lipschitz assumption. We prove that the sequence generated by the first algorithm converges weakly to a solution of the split common fixed point problem and the second one converges strongly. Moreover, the sequence { x n } generated by Algorithm 3 strongly converges to z = proj S 0 , which is the minimum-norm solution of problem (1). Numerical examples are included.

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“…In [7,9,10], it has been shown that the SPF (1.1) can also be used to model the intensity-modulated radiation therapy. Various iterative algorithms have been studied to solve the SFP (1.1), see, e.g., [8,14,16,18,22,25,27,[30][31][32] and the references therein. In particular, Jung [16] introduced iterative algorithms based on the Yamada's hybrid steepest descent method [28] for solving SFP (1.1).…”

Section: Introductionmentioning

confidence: 99%

Hybrid iterative algorithms for the split common fixed point problems

Jung¹

2017

J. Nonlinear Sci. Appl.

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In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) based on the hybrid steepest descent method for solving the split common fixed point problems. We establish the strong convergence of the sequences generated by the proposed algorithms to a solution of the split common fixed point problems, which is also a solution of a certain variational inequality. In particular, the minimum norm solution of the split common fixed point problems is obtained. As applications, variational problems and equilibrium problems are considered. c 2017 All rights reserved.Keywords: Split common fixed point problem, firmly nonexpansive mapping, nonexpansive mapping, variational inequality, minimum-norm, ρ-Lipschitzian and η-strongly monotone operator, bounded linear operator, variational problems, equilibrium problems, iterative algorithms. 2010 MSC: 47J05, 49J40, 49J52, 47J20, 47H10.

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Composite projection algorithms for the split feasibility problem

Cited by 7 publications

References 35 publications

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

Iterative Algorithms for Split Common Fixed Point Problem Involved in Pseudo-Contractive Operators without Lipschitz Assumption

Hybrid iterative algorithms for the split common fixed point problems

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