New modifications of conjugate gradient coefficient with global convergence properties

Conjugate gradient (CG) methods have played an important role in solving unconstrained optimization due to its simplicity and global convergence properties. In this paper, two new modifications of conjugate gradient coefficient (β_k) with global convergence properties are presented. The global convergence result is established using exact line searches. Comparisons are made between six others well known CG coefficient. Preliminary result by performance profile shows that the proposed formula is competitive when compared to the other CG coefficients.