Abstract
In this article, we propose a new line search method for solving unconstrained optimization problems in that we combine a nonmonotone strategy into a modified Armijo rule and design a new algorithm that possibly chooses a larger steplength. This can decrease the number of iterations and function evaluations and can improve the efficiency of the algorithm. The global convergence and convergence rate are analysed under some suitable conditions. Preliminary numerical experiments establish that the new approach is robust and efficient for unconstrained optimization problems.
Acknowledgements
The authors are very grateful to the two anonymous referees for their valuable comments, which have improved this article greatly.