Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition
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- Yabe, H. & Takano, M. Computational Optimization and Applications (2004) 28: 203. doi:10.1023/B:COAP.0000026885.81997.88
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Conjugate gradient methods are appealing for large scale nonlinear optimization problems. Recently, expecting the fast convergence of the methods, Dai and Liao (2001) used secant condition of quasi-Newton methods. In this paper, we make use of modified secant condition given by Zhang et al. (1999) and Zhang and Xu (2001) and propose a new conjugate gradient method following to Dai and Liao (2001). It is new features that this method takes both available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective function. The method is shown to be globally convergent under some assumptions. Numerical results are reported.