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

• 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
• DOI: 10.1080/02331934.2020.1846188

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.