@article{Guo2024, 
author = {Xiao Guo and Chuanpei Xu and Zhibin Zhu and Benxin Zhang},
title = {Nonmonotone variable metric Barzilai-Borwein method for composite minimization problem},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {16335-16353},
keywords = {variable metric, Barzilai-Borwein method, nonsmooth optimization, total variation},
url = {https://www.sciopen.com/article/10.3934/math.2024791},
doi = {10.3934/math.2024791},
abstract = {In this study, we develop a nonmonotone variable metric Barzilai-Borwein method for minimizing the sum of a smooth function and a convex, possibly nondifferentiable, function. At each step, the descent direction is obtained by taking the difference between the minimizer of the scaling proximal function and the current iteration point. An adaptive nonmonotone line search is proposed for determining the step length along this direction. We also show that the limit point of the iterates sequence is a stationary point. Numerical results with parallel magnetic resonance imaging, Poisson, and Cauchy noise deblurring demonstrate the effectiveness of the new algorithm.}
}