Extended hybrid conjugate gradient method for unconstrained optimization

Abstract

In this paper, a new search direction vectors are defined for BFGS-CG proposed by Ibrahim et al. by combining it with a term from the search direction vector expression proposed in modified PRP scheme of Zhang et al. in order to keep the descent property of the scheme. In addition, an update parameter of PRP is proposed to improve the performance of the algorithm. This new scheme known as Extended Hybrid BFGS – CG (EHCG) method is globally convergent with Armijo-type line search. Preliminary numerical results show that the method is efficient when subjected to comparison with classical PRP, modified PRP and conventional BFGS – CG algorithms.

Keywords: Global convergence, Hybrid Conjugate Gradient Method, Sufficient Descent Condition, Unconstrained Optimization