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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Vydáno v:Applied numerical mathematics Ročník 193; s. 179 - 195
Hlavní autoři: Cheng, Wanyou, LinPeng, Zhuanghan, Li, Donghui
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2023
Témata:
[formula omitted] optimization
Proximity operator
Quasi-Newton
Quasi-Newton
ℓ1 optimization
Proximity operator
ISSN:0168-9274, 1873-5460
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Shrnutí: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