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

Abstract

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 eigenvalues in the Hessian approximation matrices of the objective function f(x).It has been proved that these algorithms have a global and superlinear convergences when f(x)is non-convex.In this paper we are going to propose a new self-scaling VMalgorithm 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.