Splitting proximal with penalization schemes for additive convex hierarchical minimization problems. (1st November 2020)

• Record Type: Journal Article
• Authors: Nimana, Nimit; Petrot, Narin
• Is Part Of: Optimization methods and software. Volume 35:Number 6(2020)
• Page Start: 1098
• Page End: 1118
• Publication Date: 2020-11-01
• Subjects: Additive convex hierarchical minimization -- convex optimization -- penalization -- proximal algorithm -- regularized least squares problems; 47H05 -- 65K05 -- 65K10 -- 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1556660
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We consider a splitting proximal algorithm with penalization for minimizing a finite sum of proper, convex and lower semicontinuous functions subject to the set of minimizers of another proper, convex and lower semicontinuous function. We show convergences of the generated sequence of iterates to an optimal solution of the considered convex hierarchical minimization problem. Some numerical experiments on the regularized least squares problems are given to show the effectiveness of the obtained theoretical results.