Hybrid Steepest-Descent Methods for Solving Variational Inequalities Governed by Boundedly Lipschitzian and Strongly Monotone Operators
Songnian He, Xiao-Lan Liang · Fixed Point Theory and Applications · 2010
Abstract Let "Equation missing" be a real Hilbert space and let "Equation missing" be a boundedly Lipschitzian and strongly monotone operator. We design three hybrid steepest descent algorithms for solving variational inequality "Equation missing" of finding a point "Equation missing" such that "Equation missing", for all "Equation missing", where "Equation missing" is the set of fixed points of a strict pseudocontraction, or the set of common fixed points of finite strict pseudocontractions. Strong convergence of the algorithms is proved.