Incremental proximal gradient scheme with penalization for constrained composite convex optimization problems. (3rd June 2021)

• Record Type: Journal Article
• Authors: Petrot, Narin; Nimana, Nimit
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1307
• Page End: 1336
• Publication Date: 2021-06-03
• Subjects: Convex optimization -- Fenchel conjugate -- incremental proximal method -- penalization -- proximal gradient algorithm; 47H05 -- 65K05 -- 65K10 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1846188
• Languages: English
• ISSNs: 0233-1934

Abstract

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.