An inexact quasi-Newton algorithm for large-scale ℓ1 optimization with box constraints

In this paper, we develop an inexact quasi-Newton algorithm for ℓ1-regularization optimization problems subject to box constraints. The algorithm uses the identification technique of the proximal gradient algorithm to estimate the active set and free variables. To accelerate the convergence, we util...

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Bibliographic Details
Published in:	Applied numerical mathematics Vol. 193; pp. 179 - 195
Main Authors:	Cheng, Wanyou, LinPeng, Zhuanghan, Li, Donghui
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.11.2023
Subjects:	[formula omitted] optimization Proximity operator Quasi-Newton Quasi-Newton ℓ1 optimization Proximity operator
ISSN:	0168-9274, 1873-5460
Online Access:	Get full text
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Summary:	In this paper, we develop an inexact quasi-Newton algorithm for ℓ1-regularization optimization problems subject to box constraints. The algorithm uses the identification technique of the proximal gradient algorithm to estimate the active set and free variables. To accelerate the convergence, we utilize the inexact quasi-Newton algorithm to update free variables. Under certain conditions, we show that the sequence generated by the algorithm converges R-linearly to a first-order optimality point of the problem. Moreover, the corresponding sequence of objective function values is also linearly convergent. Experiment results demonstrate the competitiveness of the proposed algorithm.
ISSN:	0168-9274 1873-5460
DOI:	10.1016/j.apnum.2023.07.004