Global convergence results of a new three-term memory gradient method

In this paper, a new class of three-term memory gradient methods with Armijo-like step size rule for unconstrained optimization is presented. Global convergence properties of the new methods are discussed without assuming that the sequence {xk} of iterates is bounded. Moreover, it is shown that, when f(x) is pseudo-convex (quasi-convex) function, this new method has strong convergence results. Combining FR, PR, HS methods with our new method, FR, PR, HS methods are modified to have global convergence property. Numerical results show that the new algorithms are efficient.