Incremental proximal gradient scheme with penalization for constrained composite convex optimization problems

We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with smooth penalization technique is proposed. We show the conv...

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Veröffentlicht in:Optimization Jg. 70; H. 5-6; S. 1307 - 1336
Hauptverfasser: Petrot, Narin, Nimana, Nimit
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia Taylor & Francis 03.06.2021
Taylor & Francis LLC
Schlagworte:
Algorithms
Computational geometry
Constraints
Convex analysis
Convex optimization
Convexity
Fenchel conjugate
incremental proximal method
Optimization
penalization
proximal gradient algorithm
ISSN:0233-1934, 1029-4945
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Zusammenfassung:We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with smooth penalization technique is proposed. We show the convergence of the generated sequence of iterates to an optimal solution of the optimization problems, provided that a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. Finally, the functionality of the method is illustrated by some numerical experiments addressing image inpainting problems and generalized Heron problems with least squares constraints.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1846188