Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems. (4th March 2023)

• Record Type: Journal Article
• Authors: Ogwo, G. N.; Alakoya, T. O.; Mewomo, O. T.
• Is Part Of: Optimization. Volume 72:Number 3(2023)
• Page Start: 677
• Page End: 711
• Publication Date: 2023-03-04
• Subjects: Minimization problem -- quasi-pseudocontractive mappings -- Lipschitzian -- fixed point problem -- iterative scheme; 47H09 -- 47H10 -- 49J20 -- 49J40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1981897
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature.