New Scaled Three-Term Memoryless vm-Methods for Solving Nonlinear Unconstraint Problems

Abstract

Four new scaled three-term memoryless VM methods for solving nonlinear unconstrained problems are presented. The basic idea is to deal with Al-Bayati's (1991) and Biggs's (1983) self-scaling VMupdates in the frame of new scaled CG-methods. Birgin-Martinez (2001) and Abbo (2007) positive parameters are used to scale these spectral CG-methods. The new search directions are reset to the standard Steepest Descent (SD) direction when Powell's (1977) restarting criterion holds. Andrei's (2010) acceleration scheme of the step-size parameter has been employed in the new proposed methods to improve the efficiency of such methods. Under common assumptions; the new methods are proved to be globally convergent. Computational results for a set consisting of 100 unconstrained optimization test problems show that the new methods substantially outperforms the scaled memoryless BFGS method.