A new family of conjugate gradient methods

  • Authors:

  • Zhen-Jun Shi;Jinhua Guo

  • Affiliations:

  • College of Operations Research and Management, Qufu Normal University, Rizhao, Shandong 276826, PR China and Department of Computer and Information Science, University of Michigan, Dearborn, MI 48 ...;Department of Computer and Information Science, University of Michigan, Dearborn, MI 48128-1491, USA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2009

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Abstract

In this paper we develop a new class of conjugate gradient methods for unconstrained optimization problems. A new nonmonotone line search technique is proposed to guarantee the global convergence of these conjugate gradient methods under some mild conditions. In particular, Polak-Ribiere-Polyak and Liu-Storey conjugate gradient methods are special cases of the new class of conjugate gradient methods. By estimating the local Lipschitz constant of the derivative of objective functions, we can find an adequate step size and substantially decrease the function evaluations at each iteration. Numerical results show that these new conjugate gradient methods are effective in minimizing large-scale non-convex non-quadratic functions.