New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process

Andreea Bejenaru and Mihai Postolache ()
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Andreea Bejenaru: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mihai Postolache: Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 19, 1-16

Abstract: Split variational inclusions are revealed as a large class of problems that includes several other pre-existing split-type issues: split feasibility, split zeroes problems, split variational inequalities and so on. This makes them not only a rich direction of theoretical study but also one with important and varied practical applications: large dimensional linear systems, optimization, signal reconstruction, boundary value problems and others. In this paper, the existing algorithmic tools are complemented by a new procedure based on a three-step iterative process. The resulting approximating sequence is proved to be weakly convergent toward a solution. The operation mode of the new algorithm is tracked in connection with mixed optimization–feasibility and mixed linear–feasibility systems. Standard polynomiographic techniques are applied for a comparative visual analysis of the convergence behavior.

Keywords: split monotone variational inclusions; split variational inequality; split feasibility; monotone maximal operators; mixed optimization–feasibility systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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