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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Bibliographic Details
Published in:Optimization Vol. 70; no. 5-6; pp. 1307 - 1336
Main Authors: Petrot, Narin, Nimana, Nimit
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.06.2021
Taylor & Francis LLC
Subjects:
Algorithms
Computational geometry
Constraints
Convex analysis
Convex optimization
Convexity
Fenchel conjugate
incremental proximal method
Optimization
penalization
proximal gradient algorithm
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary: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.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1846188