A memory gradient method with a new nonmonotone line search rule

Based on nonmonotone Armijo line search, the paper proposes a new nonmonotone line search and investigates a memory gradient method with this line search. Its global convergence is also proved under some mild conditions. As compared with nonmonotone Armijo rule, the new nonmonotone line search can effectively reduce the function evaluations by choosing a larger accepted stepsize at each iteration so as to reduce the computation of algorithm.