A new family of conjugate gradient methods for unconstrained optimization

Conjugate gradient methods are well known and popular in unconstrained optimization. Numerous studies and modifications have been devoted by researchers to improve this method. In this paper, we introduced a new conjugate gradient coefficient (β_k) and tested its performance using exact line search. Numerical results based on number of iterations have shown our new β_k performance is better or equivalent to the other six well known β_k proposed by the early researchers. The results also suggest that this method possesses global convergence properties.