In this paper, we present a pair of CQ-algorithms solving the split feasibility problem with multiple output sets and prove their strong convergence. Various methods are used in the algorithm to improve usability and ...
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In this paper, we present a pair of CQ-algorithms solving the split feasibility problem with multiple output sets and prove their strong convergence. Various methods are used in the algorithm to improve usability and increase the iteration speed. To broaden the algorithm's usability, we incorporate an adaptive stepsize and the algorithm works based on replacing the projection to the half-space with that to the intersection of two half-spaces. To hasten the convergence process, the"dividing by norm" approach is selected and the subsequent output hinges on the prior step's outcome. Finally, our numerical tests in signal recovery demonstrate the superior efficacy of our algorithms.
The aim of this manuscript is to introduce a new self-adaptive algorithm designed to tackle the variational inequality problem over the solution set of the multiple-setssplitfeasibilityproblem with multipleoutput ...
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The aim of this manuscript is to introduce a new self-adaptive algorithm designed to tackle the variational inequality problem over the solution set of the multiple-setssplit feasibility problem with multiple output sets in Hilbert spaces. Our algorithm showcases strong convergence properties, eliminating the necessity for prior knowledge of Lipschitz and strongly monotone constants associated with the mapping. Moreover, it utilizes information from previous steps to guide its implementation, thus eliminating the necessity to compute or estimate the norm of the given operator. The paper presents various corollaries stemming from our main result. Finally, we present several numerical examples that illustrate the performance of our proposed algorithms in comparison to related algorithms.
The split feasibility problem with multiple output sets is to find a point x* is an element of boolean AND(t)(i=1) C-i such that A(j)x* is an element of Q(j), j = 1, 2, ..., r where C-i subset of H and Q(j) subset of ...
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The split feasibility problem with multiple output sets is to find a point x* is an element of boolean AND(t)(i=1) C-i such that A(j)x* is an element of Q(j), j = 1, 2, ..., r where C-i subset of H and Q(j) subset of H-j are nonempty, convex, and closed subsets, H and H-j are Hilbert spaces, and A(j) : H -> H-j are linear and bounded operators. In this paper, we present two self-adaptive ball-relaxed CQ algorithms. Under mild conditions, we establish strong convergence and provide numerical experiments to illustrate the effectiveness of the proposed algorithms.
作者：
Taddele, Guash HaileKumam, PoomRehman, Habib UrGebrie, Anteneh GetachewKMUTT
Dept Math Fac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT
Fixed Point Theory & Applicat Res Grp Ctr Excellence Theoret & Computat Sci TaCS CoE Fixed Point Res LabFac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT
Fac Sci Ctr Excellence Theoret & Computat Sci TaCS CoE 126 Pracha Uthit Rd Bangkok 10140 Thailand China Med Univ
China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan Debre Berhan Univ
Dept Math Coll Computat & Nat Sci POB 445 Debre Berhan Ethiopia
In this paper, we propose two new self-adaptive inertial relaxed CQ algorithms for solving the split feasibility problem with multiple output sets in the framework of real Hilbert spaces. The proposed algorithms invol...
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In this paper, we propose two new self-adaptive inertial relaxed CQ algorithms for solving the split feasibility problem with multiple output sets in the framework of real Hilbert spaces. The proposed algorithms involve computing projections onto half-spaces instead of onto the closed convex sets, and the advantage of the self-adaptive step size introduced in our algorithms is that it does not require the computation of operator norm. We establish and prove weak and strong convergence theorems for the iterative sequences generated by the introduced algorithms for solving the aforementioned problem. Moreover, we apply the new results to solve some other problems. Finally, we present some numerical examples to illustrate the implementation of our algorithms and compared them to some existing results.
In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing...
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In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature.
In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The stron...
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In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split feasibility problem with multiple output sets in real Hilbert spaces. The strong convergence of the proposed algorithm is proved without knowing any information of the Lipschitz and strongly monotone constants of the mapping. In addition, the implementation of the algorithm does not require the computation or estimation of the norms of the given bounded linear operators. Special cases are considered. Finally, a numerical experiment has been carried out to illustrate the proposed algorithm.
In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multipleoutputsets for demicontractive mappin...
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In this paper, we investigate the problem of solving strongly monotone variational inequality problems over the solution set of the split common fixed point problem with multipleoutputsets for demicontractive mappings in real Hilbert spaces. The strong convergence of the iterative sequence generated by the algorithm method is established without the prior knowledge of the norms of the given bounded linear operators. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, we include several numerical examples that serve to illustrate the performance of our proposed algorithm.
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