GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

Changyu WANG;Meixia LI

系统科学与复杂性(英文) ›› 2007, Vol. 20 ›› Issue (3) : 416-428.

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系统科学与复杂性(英文) ›› 2007, Vol. 20 ›› Issue (3) : 416-428.
论文

GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

    Changyu WANG(1), Meixia LI(2)
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GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS

    Changyu WANG(1), Meixia LI(2)
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摘要

In this paper, the authors propose a class of Dai-Yuan (abbr.DY) conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk+1=xk+αk(sk+ωk), where the main direction sk is obtained by DY conjugate gradient method,ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit
necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.

Abstract

In this paper, the authors propose a class of Dai-Yuan (abbr.DY) conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is xk+1=xk+αk(sk+ωk), where the main direction sk is obtained by DY conjugate gradient method,ωk is perturbation term, and stepsize αk is determined by linesearch which does not tend to zero in the limit
necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.

关键词

Conjugate gradient method / global convergence / perturbation / uniformly convex.

Key words

Conjugate gradient method / global convergence / perturbation / uniformly convex.

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Changyu WANG , Meixia LI. GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS. 系统科学与复杂性(英文), 2007, 20(3): 416-428
Changyu WANG , Meixia LI. GLOBAL CONVERGENCE OF THE DAI-YUAN CONJUGATE GRADIENT METHOD WITH PERTURBATIONS. Journal of Systems Science and Complexity, 2007, 20(3): 416-428
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