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Decentralized gradient algorithm for solution of a linear equation
1. | College of Engineering and Computer Science, The Australian National University, Canberra, Australia |
2. | School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, United States |
3. | Department of Electrical Engineering, Yale University, New Haven, CT, United States |
4. | Institute for Mathematics, University of Würzburg, Emil-Fischer Straße 40, 97074 Würzburg |
References:
[1] |
C. Anderson, Solving linear eqauations on parallel distributed memory architectures by extrapolation,, Technical Report, (1997). Google Scholar |
[2] |
O. Axelsson, Iterative Solution Methods,, Cambridge University Press, (1996).
doi: 10.1017/CBO9780511624100. |
[3] |
T. Chang, A. Nedic and A. Scaglione, Distributed constrained optimization by consensus-based primal-dual perturbation method,, \emph{IEEE Transactions on Automatic Control}, 59 (2014), 1524.
doi: 10.1109/TAC.2014.2308612. |
[4] |
F. R. K. Chung, Spectral Graph Theory,, American Mathematical Society, (1997).
|
[5] |
J. C. Duchi, A. Agarwal and M. J. Wainwright, Dual averaging for distributed optimization: Convergence analysis and network scaling,, \emph{IEEE Transactions on Automatic Control}, 57 (2012), 592.
doi: 10.1109/TAC.2011.2161027. |
[6] |
A. Edelman, Large dense numerical linear algebra in 1993: The Parallel Computing Influence,, Technical Report, (1993). Google Scholar |
[7] |
U. Helmke and J. B. Moore, Optimization and Dynamical Systems,, Communications and Control Engineering, (1994).
doi: 10.1007/978-1-4471-3467-1. |
[8] |
R. A. Horn and C. R. Johnson, Matrix Analysis,, Cambridge University Press, (1985).
doi: 10.1017/CBO9780511810817. |
[9] |
D. Jakovetic, J. M. F. Moura and J. Xavier, Fast distributed gradient methods,, \emph{IEEE Transactions on Automatic Control}, 59 (2014), 1131.
doi: 10.1109/TAC.2014.2298712. |
[10] |
S. Kar, J. M. F. Moura and K. Ramanan, Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication,, \emph{IEEE Transactions on Information Theory}, 58 (2012), 1.
doi: 10.1109/TIT.2012.2191450. |
[11] |
K. Kurdyka, T. Mostowski and A. Parusinski, Proof of the gradient conjecture of R. Thom,, \emph{Annals of Mathematics}, 152 (2000), 763.
doi: 10.2307/2661354. |
[12] |
S. Lojasiewicz, Sur les trajectoires du gradient dune fonction analytique,, \emph{Seminari di Geometria, (1984), 115.
|
[13] |
D. G. Luenberger, Optimization by Vector Space Methods,, John Wiley and Sons, (1969).
|
[14] |
R. Mehmood and J. Crowcroft, Parallel Iterative Solution Method of Large Sparse Linear Equation Systems,, Technical Report, (2005). Google Scholar |
[15] |
B. Mohar, The Laplacian spectrum of graphs,, \emph{Graph Theory, (1991), 871.
doi: 10.1.1.96.2577. |
[16] |
S. Mou, A. S. Morse, Z. Lin, L. Wang and D. Fullmer, A distributed algorithm for efficiently solving linear equations and its applications,, \emph{Systems and Control Letters}, (2015). Google Scholar |
[17] |
S. Mou and A. S. Morse, A fixed-neighbor,distributed algorithm for solving a linear algebraic equation,, \emph{European Control Conference}, (2013), 2269. Google Scholar |
[18] |
S. Mou, J. Liu and A. S. Morse, A distributed algorithm for solving a linear algebraic equation,, \emph{the 51st Annual Allerton Conference on Communication, (2013), 267.
|
[19] |
S. Mou, J. Liu and A. S. Morse, A distributed algorithm for solving a linear algebraic equation,, \emph{IEEE Transactions on Automatic Control}, 60 (2015), 5409.
doi: 10.1109/TAC.2015.2414771. |
[20] |
A. Nedic, A. Ozdaglar and P. A. Parrilo, Constrained consensus and optimization in multi-agent networks,, \emph{IEEE Transactions on Automatic Control}, 55 (2010), 922.
doi: 10.1109/TAC.2010.2041686. |
[21] |
A. Nedic and A. Olshevsky, Distributed optimization over time-varying directed graphs,, \emph{IEEE Transactions on Automatic Control}, 60 (2014), 601.
doi: 10.1109/TAC.2014.2364096. |
[22] |
J. J. Sylvester, On the relation between the minor determinants of linearly equivalent quadratic functions,, \emph{Phylosophical Magazine}, 1 (1851), 295.
doi: 10.1080/14786445108646735. |
[23] |
C. Wang, K. Ren, J. Wang and Q. Wang, Harnessing the cloud for securely outsourcing large-scale systems of linear equations,, \emph{IEEE Transactions on Parallel and Distributed Systems}, 24 (2013), 1172.
doi: 10.1109/TPDS.2012.206. |
show all references
References:
[1] |
C. Anderson, Solving linear eqauations on parallel distributed memory architectures by extrapolation,, Technical Report, (1997). Google Scholar |
[2] |
O. Axelsson, Iterative Solution Methods,, Cambridge University Press, (1996).
doi: 10.1017/CBO9780511624100. |
[3] |
T. Chang, A. Nedic and A. Scaglione, Distributed constrained optimization by consensus-based primal-dual perturbation method,, \emph{IEEE Transactions on Automatic Control}, 59 (2014), 1524.
doi: 10.1109/TAC.2014.2308612. |
[4] |
F. R. K. Chung, Spectral Graph Theory,, American Mathematical Society, (1997).
|
[5] |
J. C. Duchi, A. Agarwal and M. J. Wainwright, Dual averaging for distributed optimization: Convergence analysis and network scaling,, \emph{IEEE Transactions on Automatic Control}, 57 (2012), 592.
doi: 10.1109/TAC.2011.2161027. |
[6] |
A. Edelman, Large dense numerical linear algebra in 1993: The Parallel Computing Influence,, Technical Report, (1993). Google Scholar |
[7] |
U. Helmke and J. B. Moore, Optimization and Dynamical Systems,, Communications and Control Engineering, (1994).
doi: 10.1007/978-1-4471-3467-1. |
[8] |
R. A. Horn and C. R. Johnson, Matrix Analysis,, Cambridge University Press, (1985).
doi: 10.1017/CBO9780511810817. |
[9] |
D. Jakovetic, J. M. F. Moura and J. Xavier, Fast distributed gradient methods,, \emph{IEEE Transactions on Automatic Control}, 59 (2014), 1131.
doi: 10.1109/TAC.2014.2298712. |
[10] |
S. Kar, J. M. F. Moura and K. Ramanan, Distributed parameter estimation in sensor networks: Nonlinear observation models and imperfect communication,, \emph{IEEE Transactions on Information Theory}, 58 (2012), 1.
doi: 10.1109/TIT.2012.2191450. |
[11] |
K. Kurdyka, T. Mostowski and A. Parusinski, Proof of the gradient conjecture of R. Thom,, \emph{Annals of Mathematics}, 152 (2000), 763.
doi: 10.2307/2661354. |
[12] |
S. Lojasiewicz, Sur les trajectoires du gradient dune fonction analytique,, \emph{Seminari di Geometria, (1984), 115.
|
[13] |
D. G. Luenberger, Optimization by Vector Space Methods,, John Wiley and Sons, (1969).
|
[14] |
R. Mehmood and J. Crowcroft, Parallel Iterative Solution Method of Large Sparse Linear Equation Systems,, Technical Report, (2005). Google Scholar |
[15] |
B. Mohar, The Laplacian spectrum of graphs,, \emph{Graph Theory, (1991), 871.
doi: 10.1.1.96.2577. |
[16] |
S. Mou, A. S. Morse, Z. Lin, L. Wang and D. Fullmer, A distributed algorithm for efficiently solving linear equations and its applications,, \emph{Systems and Control Letters}, (2015). Google Scholar |
[17] |
S. Mou and A. S. Morse, A fixed-neighbor,distributed algorithm for solving a linear algebraic equation,, \emph{European Control Conference}, (2013), 2269. Google Scholar |
[18] |
S. Mou, J. Liu and A. S. Morse, A distributed algorithm for solving a linear algebraic equation,, \emph{the 51st Annual Allerton Conference on Communication, (2013), 267.
|
[19] |
S. Mou, J. Liu and A. S. Morse, A distributed algorithm for solving a linear algebraic equation,, \emph{IEEE Transactions on Automatic Control}, 60 (2015), 5409.
doi: 10.1109/TAC.2015.2414771. |
[20] |
A. Nedic, A. Ozdaglar and P. A. Parrilo, Constrained consensus and optimization in multi-agent networks,, \emph{IEEE Transactions on Automatic Control}, 55 (2010), 922.
doi: 10.1109/TAC.2010.2041686. |
[21] |
A. Nedic and A. Olshevsky, Distributed optimization over time-varying directed graphs,, \emph{IEEE Transactions on Automatic Control}, 60 (2014), 601.
doi: 10.1109/TAC.2014.2364096. |
[22] |
J. J. Sylvester, On the relation between the minor determinants of linearly equivalent quadratic functions,, \emph{Phylosophical Magazine}, 1 (1851), 295.
doi: 10.1080/14786445108646735. |
[23] |
C. Wang, K. Ren, J. Wang and Q. Wang, Harnessing the cloud for securely outsourcing large-scale systems of linear equations,, \emph{IEEE Transactions on Parallel and Distributed Systems}, 24 (2013), 1172.
doi: 10.1109/TPDS.2012.206. |
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