A new nonmonotone line search technique for unconstrained optimization

In this paper, a new nonmonotone line search rule is proposed,which is verified to be an improved version of the nonmonotone line search technique proposed by Zhang and Hager. Unlike the Zhang and Hager's method, our nonmonotone line search is proved to own a nice property similar to the standard Armijo line search. In virtue of such a property, global convergence is established for the developed algorithm, where the search direction is supposed to satisfy some mild conditions and the stepsize is chosen by the new line search rule. R-linear convergence of the developed algorithm is proved for strongly convex objective functions. The developed algorithm is used to solve the test problems available in the CUTEr, the numerical results demonstrate that the new line search strategy outperforms the other similar ones.