An Inertial Iterative Regularization Method for a Class of Variational Inequalities

Nguyen Buong (), Nguyen Duong Nguyen () and Nguyen Thi Quynh Anh ()
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Nguyen Buong: Institute of Theoretical and Applied Research
Nguyen Duong Nguyen: Foreign Trade University
Nguyen Thi Quynh Anh: People’s Police University of Technology and Logistics

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 2, No 6, 649-667

Abstract: Abstract In this paper, we study a class of variational inequality problems the constraint set of which is the set of common solutions of a finite family of operator equations, involving hemi-continuous accretive operators on a reflexive and strictly convex Banach space with a Gâteaux differentiable norm. We present a sequential regularization method of Lavrentiev type and an iterative regularization one in combination with an inertial term to speed up convergence. The strong convergence of the methods is proved without the co-coercivity imposed on any operator in the family. An application of our results to solving the split common fixed point problem with pseudocontractive and nonexpansive operators is given with computational experiments for illustration.

Keywords: Accretive operator; Variational inequality; Reflexive Banach space; Lavrentiev regularization; 47J05; 47H09; 49J30; 47H07; 47H10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02443-0

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