A spectral PRP conjugate gradient methods for nonconvex  optimization problem  based on modifiedline search

Zhong Wan; Chaoming Hu; Zhanlu Yang

doi:10.3934/dcdsb.2011.16.1157

Article Contents

2011, Volume 16, Issue 4: 1157-1169. Doi: 10.3934/dcdsb.2011.16.1157

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A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search

1.
School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083

Received: July 31, 2010

Revised: January 31, 2011

Published: May 2011

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Abstract

In this paper, a new spectral PRP conjugate gradient algorithm is developed for solving nonconvex unconstrained optimization problems. The search direction in this algorithm is proved to be a sufficient descent direction of the objective function independent of line search. To rule out possible unacceptably short step in the Armijo line search, a modified Armijo line search strategy is presented. The obtained step length is improved by employing the properties of the approximate Wolfe conditions. Under some suitable assumptions, the global convergence of the developed algorithm is established. Numerical experiments demonstrate that this algorithm is promising.

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Mathematics Subject Classification: Primary: 90C30, 90C53; Secondary: 65K05.

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