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

Loris Cannelli (lcannell***at***purdue.edu)
Francisco Facchinei (francisco.facchinei***at***uniroma1.it)
Vyacheslav Kungurtsev (vyacheslav.kungurtsev***at***fel.cvut.cz)
Gesualdo Scutari (gscutari***at***purdue.edu)

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.

Keywords: Asynchronous algorithms, big-data, convergence rate, nonconvex constrained optimization

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization

Category 3: Optimization Software and Modeling Systems (Parallel Algorithms )


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Entry Submitted: 01/17/2017
Entry Accepted: 01/17/2017
Entry Last Modified: 01/19/2017

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