String-Averaging Incremental Subgradients for Constrained Convex Optimization with Applications to Reconstruction of Tomographic Images
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.
Keywords
Cite
@article{arxiv.1610.05823,
title = {String-Averaging Incremental Subgradients for Constrained Convex Optimization with Applications to Reconstruction of Tomographic Images},
author = {Rafael Massambone de Oliveira and Elias Salomão Helou and Eduardo Fontoura Costa},
journal= {arXiv preprint arXiv:1610.05823},
year = {2016}
}