Gradient related algorithm with self-scaling vm-update for unconstrained optimization

الملخص EN

In this paper, a new combined extended conjugate gradient and VM methods is proposed for unconstrained large-scale numerical Optimization.

The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by AL-Bayati's 1991 VM-update to fit a new step-size using Armijo inexact line searches.

This method is based on the inexact line searches and its numerical properties are discussed using different non- linear test functions with various dimensions.

The global convergence rate of the new algorithm is investigated under few weak conditions.

Numerical experiments show that the new algorithm seems to converge faster and is superior to other similar methods in many situations.