Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems

In this paper, a class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization on a networked system are developed, where nodes in the networked system seek for a consensus that minimizes the sum of their individual objective functions through local interactions only. T...

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Bibliographic Details
Main Authors Wei, Hejie, Qu, Zhihai, Wu, Xuyang, Wang, Hao, Lu, Jie
Format Journal Article
LanguageEnglish
Published 22.03.2019
Subjects
Mathematics - Optimization and Control
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DOI10.48550/arxiv.1903.09481

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Summary:In this paper, a class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization on a networked system are developed, where nodes in the networked system seek for a consensus that minimizes the sum of their individual objective functions through local interactions only. The proposed DEAN algorithms allow each node to repeatedly perform a local approximate Newton update, which leverages tracking the global Newton direction and dissipating the discrepancies among the nodes. Under less restrictive problem assumptions in comparison with most existing second-order methods, the DEAN algorithms enable the nodes to reach a consensus that can be arbitrarily close to the optimum. Moreover, for a particular DEAN algorithm, the nodes linearly converge to a common suboptimal solution with an explicit error bound. Finally, simulations demonstrate the competitive performance of DEAN in convergence speed, accuracy, and efficiency.
DOI:10.48550/arxiv.1903.09481