Regularized hybrid iterative algorithms for triple hierarchical variational inequalities
Lu-Chuan Ceng, Ngai‐Ching Wong, Jen‐Chih Yao · Journal of Inequalities and Applications · 2014
Abstract In this paper, we introduce and study a triple hierarchical variational inequality (THVI) with constraints of minimization and equilibrium problems. More precisely, let Fix(T) be the fixed point set of a nonexpansive mapping, let MEP(Θ,φ) be the solution set of a mixed equilibrium problem (MEP), and letΓbe the solution set of a minimization problem (MP) for a convex and continuously Frechet differential functional in Hilbert spaces. We want to find a solution x∗∈Fix(T)∩MEP(Θ,φ)∩Γ of a variational inequality with a variational inequality constraint over the intersection of Fix(T) , MEP(Θ,φ) , andΓ. We propose a hybrid iterative algorithm with regularization to compute approximate solutions of the THVI, and we present the convergence analysis of the proposed iterative algorithm. MSC:49J40, 47J20, 47H10, 65K05, 47H09.