WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Strong Convergence of Modified Gradient-Projection Algorithm for Constrained Convex Minimization Problems
Authors: Ming Tian, Lihua Huang
Abstract: 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.
Search Articles
Keywords: Gradient-projection algorithm, Constrained convex minimization, General iterative method, averaged mapping, nonexpansive mapping, fixed point, variational inequality