Asynchronous parallel algorithms for nonconvex optimization

• 成果类型: Article
• 署名作者: Cannelli, Loris; Facchinei, Francisco; Kungurtsev, Vyacheslav; Scutari, Gesualdo
• 署名单位: Purdue University System; Purdue University; Sapienza University Rome; Czech Technical University Prague
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01408-w
• 发表日期: 2020
• 页码: 121-154
• 关键词: distributed methods; CONVERGENCE

摘要

We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework 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 current state-of-the-art models. Other key features of the framework are: (1) it covers in a unified way several specific solution methods; (2) it accommodates a variety of possible parallel computing architectures; and (3) it can deal with nonconvex constraints. Almost sure convergence to stationary solutions is proved, and theoretical complexity results are provided, showing nearly ideal linear speedup when the number of workers is not too large.