Accelerated Distributed Primal-Dual Dynamics using Adaptive Synchronization

This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal variables of the coupled agents, the given law accelerates the...

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Bibliographic Details
Published inarXiv.org
Main Authors Bansode, P A, Kosaraju, K C, Wagh, S R, Pasumarthy, R, Singh, N M
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.05.2019
Subjects
Adaptive systems
Convergence
Correlation analysis
Coupling
Dynamic stability
Dynamics
Hybrid systems
L2 gain
Multiagent systems
Optimization
Robustness
Saddle points
Stability analysis
Support vector machines
Synchronism
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Summary:This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal variables of the coupled agents, the given law accelerates the convergence of the proposed dynamics to the saddle-point solution. The resulting dynamics is represented as a feedback interconnected networked system that proves to be passive. The passivity properties of the proposed dynamics are exploited along with the LaSalle's invariance principle for hybrid systems, to establish asymptotic convergence and stability of the saddle-point solution. Further, the primal dynamics is analyzed for the rate of convergence and stronger convergence bounds are established, it is proved that the primal dynamics achieve accelerated convergence under the adaptive synchronization. The robustness of the proposed dynamics is quantified using L2-gain analysis and the correlation between the rate of convergence and robustness of the proposed dynamics is presented. The effectiveness of the proposed dynamics is demonstrated by applying it to solve distributed least squares and distributed support vector machines problems.
ISSN:2331-8422