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

Weijun Zhou; Youhua Zhou

doi:10.3934/jimo.2013.9.893

Article Contents

2013, Volume 9, Issue 4: 893-899. Doi: 10.3934/jimo.2013.9.893

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

Weijun Zhou^1, and
Youhua Zhou^1,

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

Received: October 31, 2012

Revised: January 31, 2013

Published: September 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C30; Secondary: 65K05.

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References

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