String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images (Q2835449)

The article is a valuable contribution to constrained convex optimization including subgradient directions and string-averaging techniques. It is about splitting data into sequences (strings) and processing a given iterate independently at each string by an incremental subgradient method (ISM). Each iterate is the average of the end-points of all strings from the previous iterates.NEWLINENEWLINEThe authors investigate sparse and large-scale non-smooth convex optimization problems such as those arising in tomographic imaging. They provide a convergence analysis under realistic, standard conditions. They compare their method to classical ISM and show that their method has better performance in terms of convergence speed which is measured as the decrease ratio of the objective function in a tomographic image reconstruction application.NEWLINENEWLINEThis article is well written, structured and explained, it contains six sections: Section 1: Introduction, Section 2: Preliminary theory, Section 3: Proposed algorithm, Section 4: Convergence analysis, Section 5: Numerical experiments, and Section 6: Final comments.NEWLINENEWLINEIn fact, future scientific work on other application of string-averaging technique to incremental subgradient algorithms with stochastic errors would be interesting.