Global Convergence of a Modified Gradient Projection Method for Convex Constrained Problems

Abstract

In this paper, the continuously differentiable optimization problem min{f(x) : x ∈ Ω}, where Ω ∈ R n is a nonempty closed convex set, the gradient projection method by Calamai and More (Math. Programming, Vol.39. P.93-116, 1987) is modified by memory gradient to improve the convergence rate of the gradient projection method is considered. The convergence of the new method is analyzed without assuming that the iteration sequence {x k } of bounded. Moreover, it is shown that, when f(x) is pseudo-convex (quasi-convex) function, this new method has strong convergence results. The numerical results show that the method in this paper is more effective than the gradient projection method.