Journal
OPTIMIZATION
Volume 70, Issue 5-6, Pages 1307-1336Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2020.1846188
Keywords
Convex optimization; Fenchel conjugate; incremental proximal method; penalization; proximal gradient algorithm
Funding
- Thailand Research Fund [RAP61K0012]
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The study introduces an algorithm combining the incremental proximal gradient method with smooth penalization technique for minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. The convergence of the algorithm is proven, and its effectiveness is demonstrated through numerical experiments.
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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