New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems

We propose new conjugate gradient formulas for computing the search directions for unconstrained optimization problems. The new formulas turn out to be the conjugate descent formula if exact line searches are made. Some formulas possess the sufficient descent property without any line searches. General convergence results for the proposed formulas with the weak Wolfe–Powell conditions are studied. We prove that some of the formulas with the steplength technique which ensures the Zoutendijk condition to be held are globally convergent. In addition, the global convergence results for some other formulas with the standard Armijo line search are also given. Preliminary numerical results show that the proposed methods are very promising.