Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part II: Complexity and Numerical Results

• Published in: arXiv.org
• Main Authors: Cannelli, Loris, Facchinei, Francisco, Kungurtsev, Vyacheslav, Scutari, Gesualdo
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 19.01.2017
• Subjects: Algorithms; Complexity; Data management; Nonlinear programming; Optimization; Probabilistic models
• ISSN: 2331-8422

We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex constraints. The proposed method hinges on successive convex approximation techniques and a novel probabilistic model that captures key elements of modern computational architectures and asynchronous implementations in a more faithful way than state-of-the-art models. In the companion paper we provided a detailed description on the probabilistic model and gave convergence results for a diminishing stepsize version of our method. Here, we provide theoretical complexity results for a fixed stepsize version of the method and report extensive numerical comparisons on both convex and nonconvex problems demonstrating the efficiency of our approach.