Hybrid Conjugate Gradient Algorithms Using Modified Secant Equations

Based on modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce hybrid conjugate gradient algorithms for unconstrained optimization problems. Our methods are hybridizations of Hestenes-Stiefel and DaiYuan conjugate gradient methods. Under proper conditions, the algorithms are globally convergent. We give a comparison of the implementations of our algorithms with two efficiently representative hybrid conjugate gradient methods proposed by Andrei using unconstrained optimization test problems from the CUTEr collection. Numerical results show that the proposed hybrid algorithms areefficient.

Keywords:

Unconstrained optimization , hybrid conjugate gradient method , modified secant equation