Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems
Lu-Chuan Ceng, Adrian Petruşel, Mu-Ming Wong, Jen‐Chih Yao · Abstract and Applied Analysis · 2014
We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.