String-Averaging Incremental Subgradients for Constrained Convex Optimization with Applications to Reconstruction of Tomographic Images

TL;DR

This paper introduces a string-averaging incremental subgradient method for large-scale non-smooth convex optimization, demonstrating improved convergence speed in tomographic image reconstruction applications.

Contribution

It proposes a novel string-averaging approach for incremental subgradient methods, enabling efficient parallel processing and improved convergence in large-scale convex problems.

Findings

Method shows faster convergence in numerical tests

Effective for large-scale tomographic image reconstruction

Provides convergence analysis under standard conditions

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.