Geodesic
Multi-agent network flows that solve linear complementarity problems
Kybernetika, Tome 54 (2018) no. 3, pp. 542-556

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In this paper, we consider linear complementarity problems with positive definite matrices through a multi-agent network. We propose a distributed continuous-time algorithm and show its correctness and convergence. Moreover, with the help of Kalman-Yakubovich-Popov lemma and Lyapunov function, we prove its asymptotic convergence. We also present an alternative distributed algorithm in terms of an ordinary differential equation. Finally, we illustrate the effectiveness of our method by simulations.
DOI : 10.14736/kyb-2018-3-0542
Classification : 68W15, 90C33
Keywords: distributed algorithm; linear complementarity problem; multi-agent network; nonsmooth algorithm; continuous-time algorithm 
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Liang, Shu; Zeng, Xianlin. Multi-agent network flows that solve linear complementarity problems. Kybernetika, Tome 54 (2018) no. 3, pp. 542-556. doi: 10.14736/kyb-2018-3-0542

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