Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization

A. E. Al-Mazrooei, A. Latif, J. C. Yao
2014 Abstract and Applied Analysis  
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
more » ... 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.
doi:10.1155/2014/587865 fatcat:r55l735bd5b6vp4y7c5fkbvhju