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 - <p style="text-align: justify;">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.</p>