An extended nonmonotone line search technique for large-scale unconstrained optimization

- New nonmonotone line search is proposed to integrate advantages of the existing ones.
- Theory of global and local convergence has been established.
- Numerical results show its efficiency for solving large-scale optimization problems.

In this paper, an extended nonmonotone line search is proposed to improve the efficiency of the existing line searches. This line search is first proved to be an extension of the classical line search rules. On the one hand, under mild assumptions, global convergence and R-linear convergence are established for the new line search rule. On the other hand, by numerical experiments, it is shown that the line search can integrate the advantages of the existing methods in searching for a suitable step-size. Combined with the spectral step-size, a class of spectral gradient algorithms are developed and employed to solve a large number of benchmark test problems from CUTEst. Numerical results show that the new line search is promising in solving large-scale optimization problems, and outperforms the other similar ones as it is combined with a spectral gradient method.