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Volume 13, Issue 2
A Modified BFGS Formula Maintaining Positive Definiteness with Armijo-Goldstein Steplengths

I. D. Coope & C. J. Price

J. Comp. Math., 13 (1995), pp. 156-160.

Published online: 1995-04

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  • Abstract

The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength satisfying certain standard conditions. The conditions proposed in the early work of Armijo and Goldstein are sometimes replaced by those recommended by Wolfe because these latter conditions automatically allow positive definiteness of some popular quasi-Newton updates to be maintained. It is shown that a slightly modified form of quasi-Newton update allows positive definiteness to be maintained even if line searches based on the Armijo-Goldstein conditions are used.

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@Article{JCM-13-156, author = {}, title = {A Modified BFGS Formula Maintaining Positive Definiteness with Armijo-Goldstein Steplengths}, journal = {Journal of Computational Mathematics}, year = {1995}, volume = {13}, number = {2}, pages = {156--160}, abstract = {

The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength satisfying certain standard conditions. The conditions proposed in the early work of Armijo and Goldstein are sometimes replaced by those recommended by Wolfe because these latter conditions automatically allow positive definiteness of some popular quasi-Newton updates to be maintained. It is shown that a slightly modified form of quasi-Newton update allows positive definiteness to be maintained even if line searches based on the Armijo-Goldstein conditions are used.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9258.html} }
TY - JOUR T1 - A Modified BFGS Formula Maintaining Positive Definiteness with Armijo-Goldstein Steplengths JO - Journal of Computational Mathematics VL - 2 SP - 156 EP - 160 PY - 1995 DA - 1995/04 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9258.html KW - AB -

The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength satisfying certain standard conditions. The conditions proposed in the early work of Armijo and Goldstein are sometimes replaced by those recommended by Wolfe because these latter conditions automatically allow positive definiteness of some popular quasi-Newton updates to be maintained. It is shown that a slightly modified form of quasi-Newton update allows positive definiteness to be maintained even if line searches based on the Armijo-Goldstein conditions are used.

I. D. Coope & C. J. Price. (1970). A Modified BFGS Formula Maintaining Positive Definiteness with Armijo-Goldstein Steplengths. Journal of Computational Mathematics. 13 (2). 156-160. doi:
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