Accelerated gradient methods and dual decomposition in distributed model predictive control

Pontus Giselsson; Dang Doan; Tamas Keviczky; Bart De Schutter; Anders Rantzer

doi:10.1016/j.automatica.2013.01.009

Accelerated gradient methods and dual decomposition in distributed model predictive control

Pontus Giselsson, Dang Doan, Tamas Keviczky, Bart De Schutter, Anders Rantzer

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Abstract

We propose a distributed optimization algorithm for mixed
L_1/L_2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1/k^2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1/k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed model predictive control (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.

Original language	English
Pages (from-to)	829-833
Journal	Automatica
Volume	49
Issue number	3
DOIs	https://doi.org/10.1016/j.automatica.2013.01.009
Publication status	Published - 2013

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key= gis2012aut

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Control Engineering

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10.1016/j.automatica.2013.01.009

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Holmqvist, A. (Researcher), Andersson, N. (Researcher), Cervin, A. (Researcher), Mannesson, A. (Researcher), Gattami, A. (Researcher), Ghulchak, A. (Researcher), Papadopoulos, A. V. (Researcher), Rantzer, A. (Researcher), Robertsson, A. (Researcher), Sootla, A. (Researcher), THEORIN, A. (Researcher), Bernhardsson, B. (Researcher), Olofsson, B. (Researcher), Wittenmark, B. (Researcher), Grussler, C. (Researcher), Johnsson, C. (Researcher), MADJIDIAN, D. (Researcher), Johannesson, E. (Researcher), Magnusson, F. (Researcher), Ståhl, F. (Researcher), Como, G. (Researcher), Chasparis, G. (Researcher), Turesson, G. (Researcher), Dressler, I. (Researcher), Åkesson, J. (Researcher), Cho, J. H. (Researcher), Årzén, K.-E. (Researcher), Åström, K. J. (Researcher), Sou, K. C. (Researcher), Mårtensson, K. (Researcher), Berntorp, K. (Researcher), Soltesz, K. (Researcher), Lessard, L. (Researcher), Hast, M. (Researcher), Rönn, M. (Researcher), Ansbjerg Kjær, M. (Researcher), Maggio, M. (Researcher), Kristalny, M. (Researcher), Garpinger, O. (Researcher), From, P. J. (Researcher), Larsson, P.-O. (Researcher), Giselsson, P. (Researcher), Johansson, R. (Researcher), Hägglund, T. (Researcher), Vladimerou, V. (Researcher), Romero Segovia, V. (Researcher), Aurelius, A. (Researcher), Cedersjö, G. (Researcher), Bür, K. (Researcher), Dellkrantz, M. (Researcher), Du, M. (Researcher), Amani, P. (Researcher), Larsson, R. (Researcher), Tärneberg, W. (Research student), Li, Z. (Researcher), Yin, L. (Researcher), Tufvesson, F. (Researcher), Höst, S. (Researcher), Nilsson, B. (Researcher), Stenström, S. (Researcher), Andersson, J. A. (Researcher), Diehl, S. (Researcher), Dürango, J. (Researcher), Ghazaei Ardakani, M. (Researcher), Forsberg, P.-O. (Researcher), Bengtsson, F. (Researcher), Jörntell, H. (Researcher), Arévalo, C. (Researcher), Führer, C. (Researcher), Andersson, C. (Researcher), Mohammadi, F. (Researcher), Ödling, P. (Researcher), Andersson, M. (Researcher), Kihl, M. (Researcher) & Tunestål, P. (Researcher)
2008/07/01 → 2018/06/30
Project: Research

Cite this

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title = "Accelerated gradient methods and dual decomposition in distributed model predictive control",

abstract = "We propose a distributed optimization algorithm for mixed L_1/L_2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1/k^2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1/k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed model predictive control (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.",

author = "Pontus Giselsson and Dang Doan and Tamas Keviczky and {De Schutter}, Bart and Anders Rantzer",

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AU - Giselsson, Pontus

AU - Doan, Dang

AU - Keviczky, Tamas

AU - De Schutter, Bart

AU - Rantzer, Anders

N1 - key= gis2012aut

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N2 - We propose a distributed optimization algorithm for mixed L_1/L_2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1/k^2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1/k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed model predictive control (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.

AB - We propose a distributed optimization algorithm for mixed L_1/L_2-norm optimization based on accelerated gradient methods using dual decomposition. The algorithm achieves convergence rate O(1/k^2), where k is the iteration number, which significantly improves the convergence rates of existing duality-based distributed optimization algorithms that achieve O(1/k). The performance of the developed algorithm is evaluated on randomly generated optimization problems arising in distributed model predictive control (DMPC). The evaluation shows that, when the problem data is sparse and large-scale, our algorithm can outperform current state-of-the-art optimization software CPLEX and MOSEK.

U2 - 10.1016/j.automatica.2013.01.009

DO - 10.1016/j.automatica.2013.01.009

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SN - 0005-1098

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EP - 833

JO - Automatica

JF - Automatica

IS - 3

ER -

Accelerated gradient methods and dual decomposition in distributed model predictive control

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