Geodesic
Multi-agent network flows that solve linear complementarity problems
Kybernetika, Tome 54 (2018) no. 3, pp. 542-556
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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 
@article{10_14736_kyb_2018_3_0542,
     author = {Liang, Shu and Zeng, Xianlin},
     title = {Multi-agent network flows that solve linear complementarity problems},
     journal = {Kybernetika},
     pages = {542--556},
     year = {2018},
     volume = {54},
     number = {3},
     doi = {10.14736/kyb-2018-3-0542},
     mrnumber = {3844831},
     zbl = {06987021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0542/}
}
TY  - JOUR
AU  - Liang, Shu
AU  - Zeng, Xianlin
TI  - Multi-agent network flows that solve linear complementarity problems
JO  - Kybernetika
PY  - 2018
SP  - 542
EP  - 556
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0542/
DO  - 10.14736/kyb-2018-3-0542
LA  - en
ID  - 10_14736_kyb_2018_3_0542
ER  - 
%0 Journal Article
%A Liang, Shu
%A Zeng, Xianlin
%T Multi-agent network flows that solve linear complementarity problems
%J Kybernetika
%D 2018
%P 542-556
%V 54
%N 3
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-3-0542/
%R 10.14736/kyb-2018-3-0542
%G en
%F 10_14736_kyb_2018_3_0542
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

[1] Aubin, J. P., Cellina, A.: Differential Inclusions. Springer-Verlag, Berlin 1984. | DOI | MR

[2] Cherukuri, A., Cortés, J.: Initialization-free distributed coordination for economic dispatch under varying loads and generator commitment. Automatica 74 (2016), 183-193. | DOI | MR

[3] Dong, J.-L., Gao, J., Ju, F., Shen, J.: Modulus methods for nonnegatively constrained image restoration. SIAM J. Imaging Sci. 9 (2016), 1226-1246. | DOI | MR

[4] Elfoutayeni, Y., Khaladi, M.: Using vector divisions in solving the linear complementarity problem. J. Comput. Appl. Math. 236 (2012), 1919-1925. | DOI | MR

[5] Herceg, M., Jones, C. N., Kvasnica, M., Morari, M.: Enumeration-based approach to solving parametric linear complementarity problems. Automatica 62 (2015), 243-248. | DOI | MR

[6] Hu, M.-C., Lu, S.-Y., Chen, Y.-H.: Stochastic-multiobjective market equilibrium analysis of a demand response program in energy market under uncertainty. Appl. Energy 182 (2016), 500-506. | DOI

[7] Huyen, D. T. K., Yen, N. D.: Coderivatives and the solution map of a linear constraint system. SIAM J. Optim. 26 (2016), 986-1007. | DOI | MR

[8] Khalil, H. K.: Nonlinear Systems. Third edition. Prentice Hall, New Jersey, 2002.

[9] Liang, S., Yi, P., Hong, Y.: Distributed {N}ash equilibrium seeking for aggregative games with coupled constraints. Automatica 85 (2017), 179-185. | DOI | MR

[10] Liu, C., Li, C.: Synchronous and asynchronous multisplitting iteration schemes for solving mixed linear complementarity problems with {H}-matrices. J. Optim. Theory Appl. 171 (2016), 169-185. | DOI | MR

[11] Liu, J., Morse, A. S., Nedić, A., Basar, T.: Exponential convergence of a distributed algorithm for solving linear algebraic equations. Automatica 83 (2017), 37-46. | DOI | MR

[12] Liu, Q., Yang, S., Wang, J.: A collective neurodynamic approach to distributed constrained optimization. IEEE Trans. Neural Networks Learning Systems 28 (2017), 1747-1758. | DOI | MR

[13] Lou, Y., Hong, Y., Wang, S.: Distributed continuous-time approximate projection protocols for shortest distance optimization problems. Automatica 69 (2016), 289-297. | DOI | MR | Zbl

[14] Mei, S., Wei, W., Liu, F.: On engineering game theory with its application in power systems. Control Theory Technol. 15 (2017), 1-12. | DOI | MR

[15] Najafi, H. S., Edalatpanah, S.: On the convergence regions of generalized accelerated overrelaxation method for linear complementarity problems. J. Optim. Theory Appl. 156 (2013), 859-866. | DOI | MR

[16] Peng, H., Li, F., Zhang, S., Chen, B.: A novel fast model predictive control with actuator saturation for large-scale structures. Computers Structures 187 (2017), 35-49. | DOI

[17] Posa, M., Cantu, C., Tedrake, R.: A direct method for trajectory optimization of rigid bodies through contact. Int. J. Robotics Res. 33 (2014), 69-81. | DOI

[18] Reddy, P. V., Zaccour, G.: Feedback Nash equilibria in linear-quadratic difference games with constraints. IEEE Trans. Automat. Control 62 (2017), 590-604. | DOI | MR

[19] Cottle, R. W., Pang, Jong-Shi, Stone, R. E.: The Linear Complementarity Problem. SIAM, Commonwealth of Pennsylvania, 2009. | DOI

[20] Rockafellar, R. T., Wets, R. J. B.: Variational Analysis. Springer-Verlag, New York, 1998. | DOI | Zbl

[21] Sessa, V., Iannelli, L., Vasca, F.: A complementarity model for closed-loop power converters. IEEE Trans. Power Electron. 29 (2014), 6821-6835. | DOI

[22] Shi, G., Anderson, B. D. O., Helmke, U.: Network flows that solve linear equations. IEEE Trans. Automat. Control 62 (2017), 2659-2674. | DOI | MR

[23] Simantiraki, E. M., Shanno, D. F.: An infeasible-interior-point method for linear complementarity problems. SIAM J. Optim. 7 (1997), 620-640. | DOI | MR

[24] Tonge, R., Benevolenski, F., Voroshilov, A.: Mass splitting for jitter-free parallel rigid body simulation. ACM Trans. Graphics 31 (2012), 4, 1-8. | DOI

[25] Wang, Y., Lin, P., Hong, Y.: Distributed regression estimation with incomplete data in multi-agent networks. Science China Inform. Sci. 61 (2018), 092202. | DOI | MR

[26] Xie, Y., Shanbhag, U. V.: On robust solutions to uncertain linear complementarity problems and their variants. SIAM J. Optim. 26 (2016), 2120-2159. | DOI | MR

[27] Xu, P., Cannon, E., Lachapelle, G.: Stabilizing ill-conditioned linear complementarity problems. J. Geodesy 73 (1999), 204-213. | DOI

[28] Yao, J., Adler, I., Oren, S. S.: Modeling and computing two-settlement oligopolistic equilibrium in a congested electricity network. Oper. Res. 56 (2008), 34-47. | DOI | MR

[29] Yi, P., Hong, Y., Liu, F.: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and its application to economic dispatch of power systems. Automatica 74 (2016), 259-269. | DOI | MR

[30] Zeng, X., Cao, K.: Computation of linear algebraic equations with solvability verification over multi-agent networks. Kybernetika 53 (2017), 803-819. | DOI | MR

[31] Zeng, X., Liang, S., Hong, Y., Chen, J.: Distributed computation of linear matrix equations: an optimization perspective. IEEE Trans. Automat. Control, in press, arXiv preprint arXiv:1708.01833. | DOI

[32] Zeng, X., Yi, P., Hong, Y.: Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach. IEEE Trans. Automat. Control 62 (2017), 5227-5233. | DOI | MR

Cité par Sources :