Modified inertial subgradient extragradient method with self adaptive stepsize for solving monotone variational inequality and fixed point problems

• Published in: Optimization Vol. 70; no. 3; pp. 545 - 574
• Main Authors: Alakoya, T. O., Jolaoso, L. O., Mewomo, O. T.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2021; Taylor & Francis LLC
• Subjects: Adaptive algorithms; Algorithms; Convergence; Extragradient method; fixed point; Fixed points (mathematics); Half spaces; Hilbert space; inertia; Lipschitz-continuous; Mathematical analysis; monotone; Operators (mathematics); variational inequality
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2020.1723586

In this paper, we study a classical monotone and Lipschitz continuous variational inequality and fixed point problems defined on a level set of a convex function in the setting of Hilbert space. We propose a modified inertial viscosity subgradient extragradient algorithm with self-adaptive stepsize in which the two projections are made onto some half-spaces. Moreover, we obtain a strong convergence result for approximating a common solution of the variational inequality and fixed point of quasi-nonexpansive mappings under some mild conditions. The main advantages of our method are: the self adaptive step-size which avoids the need to know apriori the Lipschitz constant of the associated monotone operator, the two projections made onto some half-spaces, the strong convergence and the inertial technique employed which speeds up the rate of convergence of the algorithm. Numerical experiments are presented to demonstrate the efficiency of our algorithm in comparison with other existing algorithms in literature.