New switching algorithm for combining new multi-step CG and self-scaling VM algorithms for non-linear optimization

Abstract

New interleaved CG and self-scaling VM algorithm is presented in this research which combines Al Bayati's self-scaling VM algorithm with another new multi-step CG algorithm with inexact line searches (ILS). In an interleaving algorithm a VM-update can be initiated between each CG-step and the technique improves the rate of convergence of the new proposed algorithms. The new algorithms are tested against the standard Hestenes-Stiefel and Buckley's algorithms for a number of well-known test functions, with encouraging results.