Two New Inertial Relaxed Gradient Cq Algorithms on the Split Equality Problem

Wang, Yuanheng; Li, Xueting; Jiang, Bingnan

doi:10.11948/20210351

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…They proved that the sequence {x k } generated by (1.3) converges weakly to a solution of the MSCFP under approximate conditions. For recent inertial accelerated iterative algorithms for solving the MSFP and the MSCFP, one refers to [24,25,26] and the references therein. Inspired and motivated by the above research works, in the paper, we construct two new selfadaptive cyclic iterative algorithms for solving the MSCFP of quasi-nonexpansive operators.…”

Section: Introductionmentioning

confidence: 99%

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

2023

J. Nonlinear Var. Anal.

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In the paper, we introduce two accelerated cyclic iterative algorithms for solving the multipleset split common fixed-point problem of quasi-nonexpansive operators in real Hilbert spaces. Inspired by the primal-dual algorithm, our proposed algorithms combine inertial technique with the self-adaptive stepsizes such that the implementation of the algorithms does not need any prior information about bounded linear operator norms. The weak and strong convergence of the proposed algorithms are established under suitable assumptions. As applications, we obtain several iterative algorithms to solve the multiple-set split feasibility problem. Finally, numerical results are included to demonstrate the efficiency of the proposed iterative algorithms. Keywords. The multiple-set split common fixed-point problem, quasi-nonexpansive operators, inertial technique, the weak and strong convergence.

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Section: Introductionmentioning

confidence: 99%

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

2023

J. Nonlinear Var. Anal.

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“…It is well known that iterative methods involving monotone operators have slow convergence properties. In the literature, the study of convergence properties of iterative algorithms has become an area of contemporary interest (see, e.g., [11][12][13][14][15][16][17]). One method that is now studied enormously is the inertial extrapolation technique which dates back to the early result of Polyak [18] in the context of convex minimization.…”

Section: Introductionmentioning

confidence: 99%

Approximation method for monotone inclusion problems in real Banach spaces with applications

et al. 2022

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In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum of two monotone operators in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the sequence generated by our proposed algorithm is established by means of some new geometric inequalities proved in this paper that are of independent interest. Furthermore, numerical simulations in image restoration and compressed sensing problems are also presented. Finally, the performance of the proposed method is compared with that of some existing methods in the literature.

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Two New Inertial Relaxed Gradient Cq Algorithms on the Split Equality Problem

Cited by 2 publications

References 19 publications

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

Accelerated cyclic iterative algorithms for the multiple-set split common fixed-point problem of quasi-nonexpansive operators

Approximation method for monotone inclusion problems in real Banach spaces with applications

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