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arXiv · 1701.04900

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

Loris Cannelli·Francisco Facchinei·Vyacheslav Kungurtsev·Gesualdo Scutari
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Abstract

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.

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Loris Cannelli, Francisco Facchinei, Vyacheslav Kungurtsev, Gesualdo Scutari. 2017-01-19. Asynchronous Parallel Algorithms for Nonconvex Big-Data Optimization. Part II: Complexity and Numerical Results. https://arxiv.org/abs/1701.04900

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