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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Vydané v:Optimization Ročník 70; číslo 5-6; s. 1307 - 1336
Hlavní autori: Petrot, Narin, Nimana, Nimit
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Taylor & Francis 03.06.2021
Taylor & Francis LLC
Predmet:
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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Abstract 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.
AbstractList 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.
Author Petrot, Narin
Nimana, Nimit
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  givenname: Nimit
  orcidid: 0000-0003-1640-8919
  surname: Nimana
  fullname: Nimana, Nimit
  email: nimitni@kku.ac.th
  organization: Khon Kaen University
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SubjectTerms Algorithms
Computational geometry
Constraints
Convex analysis
Convex optimization
Convexity
Fenchel conjugate
incremental proximal method
Optimization
penalization
proximal gradient algorithm
Title Incremental proximal gradient scheme with penalization for constrained composite convex optimization problems
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