Exact penalties for decomposable convex optimization problems. (3rd September 2022)

• Record Type: Journal Article
• Authors: Konnov, I. V.
• Is Part Of: Optimization methods and software. Volume 37:Number 5(2022)
• Page Start: 1705
• Page End: 1724
• Publication Date: 2022-09-03
• Subjects: Convex optimization -- right-hand side decomposition -- exact non-smooth penalty method -- subgradient projection method -- two-speed step-size choice; 90C25 -- 90C06 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1977807
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth optimization problem. We propose to apply the exact non-smooth penalty method, which gives a solution of the initial problem under some fixed penalty parameter and provides the consistency of lower level problems. The master problem can be solved with a suitable non-smooth optimization method. The simplest of them is the custom subgradient projection method using the divergent series step-size rule without line-search, whose convergence may be, however, rather low. We suggest to enhance its step-size selection by using a two-speed rule. Preliminary results of computational experiments confirm efficiency of this technique.