Convergence Properties of a Modified BFGS Algorithm for Minimization with Armijo-Goldstein Steplengths
Year: 1999
Author: Nai-Yang Deng, Zheng-Feng Li
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 6 : pp. 645–652
Abstract
The line search strategy is crucial for an efficient unconstrained optimization algorithm. One of the reason why the Wolfe line searches is recommended lies in that it ensures positive definiteness of BFGS updates. When gradient information has to be obtained costly, the Armijo-Goldstein line searches may be preferred. To maintain positive definiteness of BFGS updates based on the Armijo-Goldstein line searches, a slightly modified form of BFGS update is proposed by I.D. Coope and C.J. Price (Journal of Computational Mathematics, 13 (1995), 156-160), while its convergence properties is open up to now. This paper shows that the modified BFGS algorithm is globally and superlinearly convergent based on the Armijo-Goldstein line searches.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1999-JCM-9135
Journal of Computational Mathematics, Vol. 17 (1999), Iss. 6 : pp. 645–652
Published online: 1999-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: BFGS methods Convergence Superlinear convergence.