String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images. (4th October 2016)

• Record Type: Journal Article
• Authors: Oliveira, Rafael Massambone de; Helou, Elias Salomão; Costa, Eduardo Fontoura
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-10-04
• Subjects: convex optimization -- incremental algorithms -- subgradient methods -- projection methods -- string-averaging algorithms; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115014
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.