A New Globally Convergent Self-Scaling Vm Algorithm for Convex and Nonconvex Optimization

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.

Keywords

• a new globally
• convergent
• self
• scaling
• vm algorithm
• convex
• nonconvex optimization