Optimal preconditioning and iteration complexity bounds for gradient-based optimization in model predictive control
Giselsson, Pontus LU
(2013)
American Control Conference, 2013
p.358-364
- Abstract
- In this paper, optimization problems arising in model predictive control (MPC) and in distributed MPC aresolved by applying a fast gradient method to the dual of the MPC optimization problem. Although the development of fast gradient methods has improved the convergence rate of gradient-based methods considerably, they are still sensitive to ill-conditioning of the problem data. Since similar optimization problems are solved several times in the MPC controller, the optimization data can be preconditioned offline to improve the convergence rate of the fast gradient method online. A natural approach to precondition the dual problem is to minimize the condition number of the Hessian matrix. However, in MPC the Hessian matrix usually becomes... (More)
- In this paper, optimization problems arising in model predictive control (MPC) and in distributed MPC aresolved by applying a fast gradient method to the dual of the MPC optimization problem. Although the development of fast gradient methods has improved the convergence rate of gradient-based methods considerably, they are still sensitive to ill-conditioning of the problem data. Since similar optimization problems are solved several times in the MPC controller, the optimization data can be preconditioned offline to improve the convergence rate of the fast gradient method online. A natural approach to precondition the dual problem is to minimize the condition number of the Hessian matrix. However, in MPC the Hessian matrix usually becomes positive semi-definite only, i.e., the condition number is infinite and cannot be minimized. In this paper, we show how to optimally precondition the optimization data by solving a semidefinite program, where optimally refers to the preconditioning that minimizes an explicit iteration complexity bound. Although the iteration bounds can be crude, numerical examples show that the preconditioning can significantly reduce the number of iterations needed to
achieve a prespecified accuracy of the solution. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3693007
- author
- Giselsson, Pontus
LU
- organization
- publishing date
- 2013
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- [Host publication title missing]
- pages
- 358 - 364
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- American Control Conference, 2013
- conference location
- Washington, DC, United States
- conference dates
- 2013-06-17 - 2016-06-19
- external identifiers
-
- wos:000327210200060
- scopus:84883532113
- ISSN
- 0743-1619
- project
- LCCC
- language
- English
- LU publication?
- yes
- id
- 69491143-e894-477b-99e1-bcdbaee4b6ce (old id 3693007)
- date added to LUP
- 2016-04-01 14:24:10
- date last changed
- 2023-11-13 07:02:04
@inproceedings{69491143-e894-477b-99e1-bcdbaee4b6ce,
abstract = {{In this paper, optimization problems arising in model predictive control (MPC) and in distributed MPC aresolved by applying a fast gradient method to the dual of the MPC optimization problem. Although the development of fast gradient methods has improved the convergence rate of gradient-based methods considerably, they are still sensitive to ill-conditioning of the problem data. Since similar optimization problems are solved several times in the MPC controller, the optimization data can be preconditioned offline to improve the convergence rate of the fast gradient method online. A natural approach to precondition the dual problem is to minimize the condition number of the Hessian matrix. However, in MPC the Hessian matrix usually becomes positive semi-definite only, i.e., the condition number is infinite and cannot be minimized. In this paper, we show how to optimally precondition the optimization data by solving a semidefinite program, where optimally refers to the preconditioning that minimizes an explicit iteration complexity bound. Although the iteration bounds can be crude, numerical examples show that the preconditioning can significantly reduce the number of iterations needed to<br/><br>
achieve a prespecified accuracy of the solution.}},
author = {{Giselsson, Pontus}},
booktitle = {{[Host publication title missing]}},
issn = {{0743-1619}},
language = {{eng}},
pages = {{358--364}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Optimal preconditioning and iteration complexity bounds for gradient-based optimization in model predictive control}},
year = {{2013}},
}