  The conjugate gradient (CG) method is widely used for solving nonlinear
unconstrained optimization problems because it requires less memory to
implement. In this paper, we propose a new parameter of the Dai Liao conjugacy
condition of the CG method with the restart property, which depends on the
Lipschitz constant and is related to the Hestenes Stiefel method. The proposed
method satisfies the descent condition and global convergence properties for
convex and non-convex functions. In the numerical experiment, we compare the
new method with CG_Descent using more than 200 functions from the CUTEst
library. The comparison results show that the new method outperforms CG Descent
in terms of CPU time, number of iterations, number of gradient evaluations, and
number of function evaluations.
