Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization
Abdullah Al-Mazrooei, Abdul Latif, Jen‐Chih Yao · Abstract and Applied Analysis · 2014
We propose implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings in a real Hilbert space. We prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets under very mild conditions.