A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization

Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011 ) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented.