Abstract
In unconstrained optimization, the original quasi-Newton condition where is the difference of the gradients at two successive iterations. Li and Fukushima proposed a modified BFGS methods based on a new Quasi –Newton equation where , where is a small positive constant .In this paper, we first propose the modified version of self-scaling VM-algorithm which was based on Li and Fukushima Quasi–Newton equation, i.e where . The corresponding AL-Bayati type algorithm is proved to possess the global convergence property in both convex and non-convex optimization problems. Experimental results indicate that the new proposed algorithm was more efficient than the standard BFGS- algorithm.