Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems

• Published in: Optimization Vol. 72; no. 3; pp. 677 - 711
• Main Authors: Ogwo, G. N., Alakoya, T. O., Mewomo, O. T.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2023; Taylor & Francis LLC
• Subjects: Adaptive algorithms; fixed point problem; Half spaces; Hilbert space; Iterative algorithms; Iterative methods; iterative scheme; Lipschitzian; Mathematical analysis; Minimization problem; Operators (mathematics); quasi-pseudocontractive mappings
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2021.1981897

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.