Multi-agent network flows that solve linear complementarity problems

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.