A new self-scaling VM-algorithm for non-convex optimization, part 1

Abstract<br /> The self-scaling VM-algorithms solves an unconstrained non-linear optimization problems by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigen-values in the Hessian approximation matrices of the objective function f(x).It has been proved that these algorithms have a global and super-linear convergences when f(x)is non- convex.<br /> In this paper we are going to propose a new self-scaling VM-algorithm with a new non-monotone line search procedure with a detailed study of the global and super-linear convergence property for the new proposed algorithm in non-convex optimization.<br /> Keywords: VM-methods, non-monotone line searches, self-scaling AL-Bayati VM- method, global converge, super-linear convergence.