An algorithm for approximating a common solution of variational inequality and convex minimization problems. (3rd October 2021)

• Record Type: Journal Article
• Authors: Nnakwe, Monday Ogudu
• Is Part Of: Optimization. Volume 70:Number 10(2021)
• Page Start: 2227
• Page End: 2246
• Publication Date: 2021-10-03
• Subjects: J-pseudocontractions -- J-fixed points -- variational inequality -- minimization problems; 47H09 -- 47H10 -- 47J25 -- 47J05 -- 37C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1777995
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Let X be a uniformly smooth and 2-uniformly convex real Banach space with dual space X ∗ . In this paper, a Halpern-type subgradient extragradient algorithm is constructed. The sequence, generated by the algorithm, converges strongly to a common solution of variational inequality and two convex minimization problems. This result is obtained as an application of a Halpern-type subgradient extragradient algorithm, for approximating a common solution of variational inequality and J -fixed points of two continuous J -pseudocontractions. The theorem proved complements, improves and unifies many recent results in the literature. Finally, numerical experiments are given to illustrate the convergence of the sequence generated by the algorithm.