A new class of nonlinear conjugate gradient coefficients with global convergence properties

Nonlinear conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. Their wide application in many fields is due to their low memory requirements and global convergence properties. Numerous studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients (βk) that possess global convergence properties is presented. The global convergence result is established using exact line searches. Numerical result shows that the proposed formula is superior and more efficient when compared to other CG coefficients.