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