A Proximal Alternating Direction Method of Multipliers for DC Programming with Structured Constraints

In this paper, we consider a class of structured DC programming, where the objective function is the difference of two (possibly nonsmooth) convex functions, and the constraint is a linear function belonging to a nonempty closed convex set. To fully exploit the favorable structure of the problem und...

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Veröffentlicht in:Journal of scientific computing Jg. 99; H. 3; S. 89
Hauptverfasser: Zhou, Yingxin, He, Hongjin, Zhang, Linan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2024
Springer Nature B.V
Schlagworte:
Algorithms
Computational Mathematics and Numerical Analysis
Convexity
Critical point
Linear functions
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical functions
Mathematics
Mathematics and Statistics
Multipliers
Operators (mathematics)
Optimization
Theoretical
Variables
Alternating direction method of multipliers
Nonconvex optimization
DC programming
90C90
90C26
Dantzig selector
Kurdyka–Łojasiewicz inequality
ISSN:0885-7474, 1573-7691
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Zusammenfassung:In this paper, we consider a class of structured DC programming, where the objective function is the difference of two (possibly nonsmooth) convex functions, and the constraint is a linear function belonging to a nonempty closed convex set. To fully exploit the favorable structure of the problem under consideration, we propose an implementable algorithm, proximal Alternating Direction Method of Multipliers (pADMM), which employs the Fenchel-Young inequality and Moreau decomposition theorem such that the potentially explicit proximal operators of the two DC parts could be efficiently explored, thereby making all subproblems quite easy in some cases. Theoretically, we prove that the sequence generated by our algorithm pADMM converges to a critical point of the problem with the help of Kurdyka–Łojasiewicz inequality. Finally, some preliminary computational results on solving ℓ 1 - α ℓ 2 -norm Dantzig selector problem and automated model selection demonstrate that our proposed method runs faster than the standard ADMM solver.
Bibliographie:ObjectType-Article-1
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-024-02550-0