New versions of the Hestenes-Stiefel nonlinear conjugate gradient method based on the secant condition for optimization

AUTOR(ES)

Zhang, Li

FONTE

Computational & Applied Mathematics

DATA DE PUBLICAÇÃO

2009

RESUMO

Based on the secant condition often satisfied by quasi-Newton methods, two new versions of the Hestenes-Stiefel (HS) nonlinear conjugate gradient method are proposed, which are descent methods even with inexact line searches. The search directions of the proposed methods have the form d k = - θkg k + βkHSd k-1, or d k = -g k + βkHSd k-1+ θky k-1. When exact line searches are used, the proposed methods reduce to the standard HS method. Convergence properties of the proposed methods are discussed. These results are also extended to some other conjugate gradient methods such as the Polak-Ribiére-Polyak (PRP) method. Numerical results are reported.

Documentos Relacionados

• A new algorithm of nonlinear conjugate gradient method with strong convergence
• On the convergence properties of the projected gradient method for convex optimization
• A new efficient nonlinear programming based method for branch overload elimination
• The global convergence of a descent PRP conjugate gradient method
• Conjugate Gradient Method for the Solution of Inverse Problems: Application in Linear Seismic Tomography