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-sets split 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.
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