American Institute of Mathematical Sciences

October  2013, 9(4): 893-899. doi: 10.3934/jimo.2013.9.893

On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization

 1 Department of Mathematics, Changsha University of Science and Technology, Changsha 410004, China, China

Received  November 2012 Revised  February 2013 Published  August 2013

In [8], Zhang et al. proposed a modified three-term HS (MTTHS) conjugate gradient method and proved that this method converges globally for nonconvex minimization in the sense that $\liminf_{k\to\infty}\|\nabla f(x_k)\|=0$ when the Armijo or Wolfe line search is used. In this paper, we further study the convergence property of the MTTHS method. We show that the MTTHS method has strongly global convergence property (i.e., $\lim_{k\to\infty}\|\nabla f(x_k)\|=0$) for nonconvex optimization by the use of the backtracking type line search in [7]. Some preliminary numerical results are reported.
Citation: Weijun Zhou, Youhua Zhou. On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization. Journal of Industrial & Management Optimization, 2013, 9 (4) : 893-899. doi: 10.3934/jimo.2013.9.893
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