A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

• Published in: Numerical algebra, control and optimization Vol. 12; no. 2; pp. 255 - 278
• Main Authors: Owolabi, Abd-semii Oluwatosin-Enitan, Alakoya, Timilehin Opeyemi, Taiwo, Adeolu, Mewomo, Oluwatosin Temitope
• Format: Journal Article
• Language: English
• Published: 01.06.2022
• Subjects: Subgradient extragradient method; Variational inequality problem; Fixed point problem; Inertial; Demicontractive mappings; Multivalued mappings
• ISSN: 2155-3297; 2155-3289; 2155-3297
• DOI: 10.3934/naco.2021004

In this paper, we present a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces. Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space. The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence. Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm.