Strong convergence of modified gradient-projection algorithm for constrained convex minimization problems

In this article, a modified gradient-projection algorithm (GPA) is introduced, which combines Xu’s idea of an alternative averaged mapping approach to the GPA and the general iterative method for nonexpansive mappings in Hilbert space introduced by Marino and Xu. Under suitable conditions, it is proved that the strong convergence of the sequences generated by implicit and explicit schemes to a solution of a constrained convex minimization problem which also solves a certain variational inequality. Obtained results extend and improve some existed results. Key–Words: Gradient-projection algorithm, Constrained convex minimization, General iterative method, averaged mapping, nonexpansive mapping, fixed point, variational inequality