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Volume 42, Issue 6
Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information

Hongzheng Ruan & Weihong Yang

DOI: 10.4208/jcm.2306-m2022-0279

J. Comp. Math., 42 (2024), pp. 1656-1687.

Published online: 2024-11

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  • Abstract

Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact. In some practical problems, we can only obtain approximate values of the objective function and its gradient. It is necessary to design optimization algorithms that can utilize inexact first-order information. In this paper, we propose an adaptive regularized quasi-Newton method to solve such problems. Under some mild conditions, we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method. Detailed implementations of our method, including the subspace technique to reduce the amount of computation, are presented. Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method, which can utilize the inexact first-order information effectively.

  • Keywords

Inexact first-order information, Regularization, Quasi-Newton method.

  • AMS Subject Headings

90C30, 68Q25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1656, author = {Ruan , Hongzheng and Yang , Weihong}, title = {Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {6}, pages = {1656--1687}, abstract = {

Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact. In some practical problems, we can only obtain approximate values of the objective function and its gradient. It is necessary to design optimization algorithms that can utilize inexact first-order information. In this paper, we propose an adaptive regularized quasi-Newton method to solve such problems. Under some mild conditions, we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method. Detailed implementations of our method, including the subspace technique to reduce the amount of computation, are presented. Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method, which can utilize the inexact first-order information effectively.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2306-m2022-0279}, url = {http://global-sci.org/intro/article_detail/jcm/23511.html} }
TY - JOUR T1 - Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information AU - Ruan , Hongzheng AU - Yang , Weihong JO - Journal of Computational Mathematics VL - 6 SP - 1656 EP - 1687 PY - 2024 DA - 2024/11 SN - 42 DO - http://doi.org/10.4208/jcm.2306-m2022-0279 UR - https://global-sci.org/intro/article_detail/jcm/23511.html KW - Inexact first-order information, Regularization, Quasi-Newton method. AB -

Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact. In some practical problems, we can only obtain approximate values of the objective function and its gradient. It is necessary to design optimization algorithms that can utilize inexact first-order information. In this paper, we propose an adaptive regularized quasi-Newton method to solve such problems. Under some mild conditions, we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method. Detailed implementations of our method, including the subspace technique to reduce the amount of computation, are presented. Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method, which can utilize the inexact first-order information effectively.

Ruan , Hongzheng and Yang , Weihong. (2024). Adaptive Regularized Quasi-Newton Method Using Inexact First-Order Information. Journal of Computational Mathematics. 42 (6). 1656-1687. doi:10.4208/jcm.2306-m2022-0279
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