Two spectral conjugate gradient methods for unconstrained optimization problems

Two new spectral conjugate gradient methods (ZL1 method and ZL2 method) for solving unconstrained optimization problems are established. Under the standard Wolfe line search, the search direction generated by the ZL1 method is a descent direction. The search direction of the ZL2 method satisfies descent property independent of the line search. The global convergence of the two new methods can be demonstrated under the standard Wolfe line search. Numerical experiments are presented to show that the two methods are effective.