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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Veröffentlicht in:Applied numerical mathematics Jg. 193; S. 179 - 195
Hauptverfasser: Cheng, Wanyou, LinPeng, Zhuanghan, Li, Donghui
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.11.2023
Schlagworte:
[formula omitted] optimization
Proximity operator
Quasi-Newton
Quasi-Newton
ℓ1 optimization
Proximity operator
ISSN:0168-9274, 1873-5460
Online-Zugang:Volltext
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Zusammenfassung: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