A New Gradient Projection Algorithm for Convex Minimization Problem and its Application to Split Feasibility Problem

Abstract

In this paper, we study convergence analysis of a new gradient projection algorithm for solving convex minimization problems in Hilbert spaces. We observe that the proposed gradient projection algorithm weakly converges to a minimum of convex function f which is defined from a closed and convex subset of a Hilbert space to $\mathbb {R}$ . Also, we give a nontrivial example to illustrate our result in an infinite dimensional Hilbert space. We apply our result to solve the split feasibility problem.