Global Convergence Properties of Nonlinear Conjugate Gradient Methods with Modified Secant Condition

Authors:
Hiroshi Yabe;Masahiro Takano
Affiliations:
Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan. yabe@rs.kagu.tus.ac.jp;National Statistics Center, 19-1 Wakamatsu-cho, Shinjuku-ku, Tokyo 162-8668, Japan
Venue:
Computational Optimization and Applications
Year:
2004

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Abstract

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.