Open AccessA new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings
Author(s) -
Abd-semii Oluwatosin-Enitan Owolabi,
Timilehin Opeyemi Alakoya,
Adeolu Taiwo,
Oluwatosin Temitope Mewomo
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.303
H-Index - 20
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021004
Subject(s) - variational inequality , mathematics , subgradient method , fixed point , hilbert space , lipschitz continuity , monotone polygon , inertial frame of reference , convergence (economics) , sequence (biology) , algorithm , strongly monotone , operator (biology) , rate of convergence , projection (relational algebra) , mathematical analysis , mathematical optimization , computer science , geometry , channel (broadcasting) , repressor , economic growth , computer network , chemistry , biology , genetics , biochemistry , quantum mechanics , transcription factor , physics , economics , gene
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.