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

In this paper,the continuously differentiable optimization problem min{f(x):x∈Ω},whereΩ∈R~n is a nonempty closed convex set,the gradient projection method by Calamai and More (Math.Pro-gramming,Vol.39.P.93-116,1987) is modified by memory gradient to improve the convergence rate of thegradient projection method is considered.The convergence of the new method is analyzed without assumingthat 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 methodin this paper is more effective than the gradient projection method.