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Keywords:
distributed computation of matrix equation; multi-agent system; sublinear convergence; stochastic mirror descent algorithm
distributed computation of matrix equation; multi-agent system; sublinear convergence; stochastic mirror descent algorithm
Summary:
In this paper, we consider a distributed stochastic computation of $AXB=C$ with local set constraints over an multi-agent system, where each agent over the network only knows a few rows or columns of matrixes. Through formulating an equivalent distributed optimization problem for seeking least-squares solutions of $AXB=C$, we propose a distributed stochastic mirror-descent algorithm for solving the equivalent distributed problem. Then, we provide the sublinear convergence of the proposed algorithm. Moreover, a numerical example is also given to illustrate the effectiveness of the proposed algorithm.
References:
[1] Bregman, L. M.: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7 (1967), 200-217. DOI | MR 0215617
[2] Chen, G., Zeng, X., Hong, Y.: Distributed optimisation design for solving the Stein equation with constraints. IET Control Theory Appl. 13 (2019), 2492-2499. DOI
[3] Cheng, S., Liang, S.: Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate. Kybernetika 56 (2020), 559-577. DOI | MR 4131743
[4] Deng, W., Zeng, X., Hong, Y.: Distributed computation for solving the Sylvester equation based on optimization. IEEE Control Systems Lett. 4 (2019), 414-419. DOI | MR 4211320
[5] Gholami, M. R., Jansson, M., al., E. G. Ström et: Diffusion estimation over cooperative multi-agent networks with missing data. IEEE Trans. Signal Inform. Process. over Networks 2 (2016), 27-289. DOI | MR 3571397
[6] Lan, G., Lee, S., Zhou, Y.: Communication-efficient algorithms for decentralized and stochastic optimization. Math. Programm. 180 (2020), 237-284. DOI | MR 4062837
[7] Lei, J., Shanbhag, U. V., al., J. S. Pang et: On synchronous, asynchronous, and randomized best-response schemes for stochastic Nash games. Math. Oper. Res. 45 (2020), 157-190. DOI | MR 4066993
[8] Liu, J., Morse, A. S., Nedic, A., a., et: Exponential convergence of a distributed algorithm for solving linear algebraic equations. Automatica 83 (2017), 37-46. DOI | MR 3680412
[9] Mou, S., Liu, J., Morse, A. S.: A distributed algorithm for solving a linear algebraic equation. IEEE Trans. Automat. Control 60 (2015), 2863-2878. DOI | MR 3419577
[10] Ram, S. S., Nedic, A., Veeravalli, V. V.: Distributed stochastic subgradient projection algorithms for convex optimization. J. Optim. Theory Appl. 147 (2010), 516-545. DOI | MR 2733992
[11] Shi, G., Anderson, B. D. O., Helmke, U.: Network flows that solve linear equations. IEEE Trans. Automat. Control 62 (2016), 2659-2674. DOI | MR 3660554
[12] Wang, Y., Lin, P., Hong, Y.: Distributed regression estimation with incomplete data in multi-agent networks. Science China Inform. Sci. 61 (2018), 092202. DOI 10.1007/s11432-016-9173-8 | MR 3742944
[13] Wang, Y., Lin, P., Qin, H.: Distributed classification learning based on nonlinear vector support machines for switching networks. Kybernetika 53 (2017), 595-611. DOI | MR 3730254
[14] Wang, Y., Zhao, W., al., Y. Hong et: Distributed subgradient-free stochastic optimization algorithm for nonsmooth convex functions over time-varying networks. SIAM J. Control Optim. 57 (2019), 2821-2842. DOI | MR 3995027
[15] Yuan, D., Hong, Y., al., D. W. C. Ho et: Optimal distributed stochastic mirror descent for strongly convex optimization. Automatica 90(2018), 196-203. DOI | MR 3764399
[16] Yuan, D., Hong, Y., al., D. W. C. Ho et: Distributed mirror descent for online composite optimization. IEEE Trans. Automat. Control (2020). MR 4210454
[17] Zeng, X., Liang, S., al., Y. Hong et: Distributed computation of linear matrix equations: An optimization perspective. IEEE Trans. Automat. Control 64 (2018), 1858-1873. DOI | MR 3951032
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