A three-parameter family of nonlinear conjugate gradient methods

In this paper, we propose a three-parameter family of conjugate gradient me thods for unconstrained optimization. The three-parameter family of methods not only includes the already existing six practical nonlinear conjugate g radient methods, but subsumes some other families of nonlinear conjugate gr adient methods as its subfamilies. With Powell's restart criterion, the thr ee-parameter family of methods with the strong Wolfe line search is shown t o ensure the descent property of each search direction. Some general conver gence results are also established for the three-parameter family of method s. This paper can also be regarded as a brief review on nonlinear conjugate gradient methods.