A method of multipliers algorithm for sparsity-promoting optimal control

Neil K. Dhingra; Mihailo R. Jovanović

doi:10.1109/ACC.2016.7525203

A method of multipliers algorithm for sparsity-promoting optimal control

Neil K. Dhingra
, Mihailo R. Jovanović

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

12 Scopus citations

Abstract

We develop a customized method of multipliers algorithm to efficiently solve a class of regularized optimal control problems. By exploiting the problem structure, we transform the augmented Lagrangian into a form which can be efficiently minimized using proximal methods. We apply our algorithm to an ℓ1-regularized state-feedback optimal control problem and compare its performance with a proximal gradient algorithm and an alternating direction method of multipliers algorithm. In contrast to other methods, our algorithm has both a theoretical guarantee of convergence and fast computation speed in practice.

Original language	English (US)
Title of host publication	2016 American Control Conference, ACC 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1942-1947
Number of pages	6
ISBN (Electronic)	9781467386821
DOIs	https://doi.org/10.1109/ACC.2016.7525203
State	Published - Jul 28 2016
Event	2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016

Publication series

Name	Proceedings of the American Control Conference
Volume	2016-July
ISSN (Print)	0743-1619

Other

Other	2016 American Control Conference, ACC 2016
Country/Territory	United States
City	Boston
Period	7/6/16 → 7/8/16

Bibliographical note

Publisher Copyright:
© 2016 American Automatic Control Council (AACC).

Keywords

Augmented Lagrangian
Method of multipliers
Non-smooth optimization
Proximal methods
Sparsity-promoting optimal control
Structure identification

Publisher link

10.1109/ACC.2016.7525203

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A method of multipliers algorithm for sparsity-promoting optimal control. / Dhingra, Neil K.; Jovanović, Mihailo R.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1942-1947 7525203 (Proceedings of the American Control Conference; Vol. 2016-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Dhingra, NK & Jovanović, MR 2016, A method of multipliers algorithm for sparsity-promoting optimal control. in 2016 American Control Conference, ACC 2016., 7525203, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 1942-1947, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525203

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abstract = "We develop a customized method of multipliers algorithm to efficiently solve a class of regularized optimal control problems. By exploiting the problem structure, we transform the augmented Lagrangian into a form which can be efficiently minimized using proximal methods. We apply our algorithm to an ℓ1-regularized state-feedback optimal control problem and compare its performance with a proximal gradient algorithm and an alternating direction method of multipliers algorithm. In contrast to other methods, our algorithm has both a theoretical guarantee of convergence and fast computation speed in practice.",

keywords = "Augmented Lagrangian, Method of multipliers, Non-smooth optimization, Proximal methods, Sparsity-promoting optimal control, Structure identification",

author = "Dhingra, \{Neil K.\} and Jovanovi{\'c}, \{Mihailo R.\}",

note = "Publisher Copyright: {\textcopyright} 2016 American Automatic Control Council (AACC).; 2016 American Control Conference, ACC 2016 ; Conference date: 06-07-2016 Through 08-07-2016",

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N2 - We develop a customized method of multipliers algorithm to efficiently solve a class of regularized optimal control problems. By exploiting the problem structure, we transform the augmented Lagrangian into a form which can be efficiently minimized using proximal methods. We apply our algorithm to an ℓ1-regularized state-feedback optimal control problem and compare its performance with a proximal gradient algorithm and an alternating direction method of multipliers algorithm. In contrast to other methods, our algorithm has both a theoretical guarantee of convergence and fast computation speed in practice.

AB - We develop a customized method of multipliers algorithm to efficiently solve a class of regularized optimal control problems. By exploiting the problem structure, we transform the augmented Lagrangian into a form which can be efficiently minimized using proximal methods. We apply our algorithm to an ℓ1-regularized state-feedback optimal control problem and compare its performance with a proximal gradient algorithm and an alternating direction method of multipliers algorithm. In contrast to other methods, our algorithm has both a theoretical guarantee of convergence and fast computation speed in practice.

KW - Augmented Lagrangian

KW - Method of multipliers

KW - Non-smooth optimization

KW - Proximal methods

KW - Sparsity-promoting optimal control

KW - Structure identification

UR - https://www.scopus.com/pages/publications/84992153644

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DO - 10.1109/ACC.2016.7525203

M3 - Conference contribution

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T3 - Proceedings of the American Control Conference

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EP - 1947

BT - 2016 American Control Conference, ACC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

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Y2 - 6 July 2016 through 8 July 2016

ER -

A method of multipliers algorithm for sparsity-promoting optimal control

Abstract

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Keywords

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