Improving the Dai-Liao parameter choices using a fixed point equation

Recently, based on a singular value analysis on the Dai--Liao conjugate gradient method, Babaie-Kafaki and Aminifard  suggested a fixed point equation. The prominent feature of  the proposed equation is that its solutions may increase numerical stability of the method  while improving the global convergence. Here, the  same fixed point equation  is employed to upgrade previously proposed choices of the Dai--Liao parameter based on the well-known functional iteration method.  Global convergence analysis is conducted and numerical experiments are done to support our discussions.

Keywords:

Unconstrained optimization , Conjugate gradient method , maximum magnification , fixed point equation , functional iteration