Fahimeh Biglari, Maghsud Solimanpur,
Scaling on the Spectral Gradient Methodl
This paper presents a new method for steplength selection in the frame
of spectral gradient methods. The steplength formula is based on the interpolation
scheme as well as some modified secant equations. The corresponding algorithm
selects the initial positive steplength per iteration according to the satisfaction of the
secant condition, and then a backtracking procedure along the negative gradient is
performed.
The numerical experience shows that this algorithm improves favorably the ef-
ficiency property of the standard Barzilai&ndashBorwein method as well as some other
recently modified Barzilai&ndashBorwein approaches.