An efficient modification of nonlinear conjugate gradient method

To solve large and small scale unconstrained optimization problems,conjugate gradient method (cg) is an interesting and active method to find the optimum point for linear and nonlinear optimization functions. wei et al. (2006) presented an efficient modification of polak-ribiere-polyak (1969) formula,since it passes the global convergence properties under several lines searches with sufficient descent condition. in this paper,we depict a new positive cg method derived from above two coefficients,the new method achieves the global convergence properties with the strong wolfe-powel,weak wolfe powell,and modified armijo line searches. the numerical computations with the strong wolfe-powell line search demonstrated the efficiency of the new formula is almost superior to other modern methods.