A Hybrid Conjugate Gradient Method Based on an Extended Least-Squares Model

Inspired by Andrei's approach of combining the conjugate gradient parameters convexly, a hybridization of the Hestenes–Stiefel and Dai–Yuan conjugate gradient methods is proposed. The hybridization parameter is determined by using the ellipsoid norm as an extension of the Euclidean norm, in a least-squares framework. Efficiency of the suggested hybrid conjugate gradient method in the sense of the Dolan–Moré performance profile is depicted as well.

Keywords:

Unconstrained optimization , conjugate gradient algorithm , least-squares model , ellipsoid norm , secant condition.