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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| Main Authors | , , , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
22.03.2019
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1903.09481 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Qu, Zhihai Lu, Jie Wu, Xuyang Wei, Hejie Wang, Hao |
| Author_xml | – sequence: 1 givenname: Hejie surname: Wei fullname: Wei, Hejie – sequence: 2 givenname: Zhihai surname: Qu fullname: Qu, Zhihai – sequence: 3 givenname: Xuyang surname: Wu fullname: Wu, Xuyang – sequence: 4 givenname: Hao surname: Wang fullname: Wang, Hao – sequence: 5 givenname: Jie surname: Lu fullname: Lu, Jie |
| BackLink | https://doi.org/10.48550/arXiv.1903.09481$$DView paper in arXiv |
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| Snippet | In this paper, a class of Decentralized Approximate Newton (DEAN) methods for
addressing convex optimization on a networked system are developed, where nodes... |
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| SubjectTerms | Mathematics - Optimization and Control |
| Title | Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems |
| URI | https://arxiv.org/abs/1903.09481 |
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