A class of nonmonotone Armijo-type line search method for unconstrained optimization

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.

Keywords:

• unconstrained optimization
• line search method
• nonmonotone strategy
• global convergence

AMS Subject Classifications::

• 90C30
• 65k05
• 65k10

Acknowledgements

The authors are very grateful to the two anonymous referees for their valuable comments, which have improved this article greatly.