Global convergece of the bfgs algorithm with nonmonotone linesearch^∗

^∗This work is supported by National Natural Science Foundation

^∗this work is supported by national natural science foundation$ef:

Abstract

In this paper based on the nonmonotone linesearch technique of Grippo, et al ([4]) we propose a class of nonmonotone linesearches which includes many linesearches used in practice. Applying this general linesearch model to the well- known BFGS algorithm. we prove. under mild conditions. its global convergence. The numerical experiment shows that nonmonotone quasi-Newton methods

Keywords:

• BFGS algorithm
• Nonmonotone linesearch
• Global Convergence

^∗This work is supported by National Natural Science Foundation

^∗This work is supported by National Natural Science Foundation

Notes

^∗This work is supported by National Natural Science Foundation