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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1157 - 1169, Volume 16, Issue 4, November 2011      doi:10.3934/dcdsb.2011.16.1157

 
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Zhong Wan - School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083, China (email)
Chaoming Hu - School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083, China (email)
Zhanlu Yang - School of Mathematics Sciences and Computing Technology, Central South University, Hunan Changsha, 410083, China (email)

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.

Keywords:  Unconstrained optimization, sufficiently descent direction, conjugate gradient, line search, global convergence.
Mathematics Subject Classification:  Primary: 90C30, 90C53; Secondary: 65K05.

Received: August 2010;      Revised: February 2011;      Available Online: August 2011.

 References