Improved Dual Decomposition for Distributed Model Predictive Control

Giselsson, Pontus

doi:10.3182/20140824-6-za-1003.00294

Cited by 9 publications

(13 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we show that these two approaches are indeed dual to each other and that they yield equivalent algorithms. This result shows that the algorithms presented in [7], [6], can be interpreted as solving a preconditioned problem using a fast dual proximal gradient method.…”

Section: Introductionmentioning

confidence: 78%

“…In [6], [7], a dual approach is taken in which no preconditioning is used, i.e. the function d remains the same, but the approximation of d used in the algorithm is instead the right hand side of…”

Section: Relation To Other Methodsmentioning

confidence: 99%

“…Related work include our recent papers [7], [6], in which a dual approach to the one taken here is presented. The idea in this paper is to use preconditioning to reshape the dual function to match the first order approximation in the algorithm.…”

Section: Introductionmentioning

confidence: 98%

“…The idea in this paper is to use preconditioning to reshape the dual function to match the first order approximation in the algorithm. In [7], [6], the approximation used in the algorithm is instead reshaped to fit the shape of the dual function. In this paper, we show that these two approaches are indeed dual to each other and that they yield equivalent algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Preconditioning in fast dual gradient methods

Giselsson

Boyd

2014

53rd IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

First order optimization methods often perform poorly on ill-conditioned optimization problems. However, by preconditioning the problem data and solving the preconditioned problem, the performance of the first order method can be significantly improved. In this paper, we show how to compute such preconditioners when solving the dual of strongly convex optimization problems using fast dual proximal gradient methods. The proposed preconditioning is evaluated by solving ill-conditioned optimization problems that arise from controlling the pitch angle in an aircraft using model predictive control. The numerical example shows improvements of two to three orders of magnitude in the fast dual proximal gradient method compared to when no preconditioning is used.

show abstract

Section: Introductionmentioning

confidence: 78%

Section: Relation To Other Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Preconditioning in fast dual gradient methods

Giselsson

Boyd

2014

53rd IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…the authors of [6], use a coordinate ascent method to solve matrix problems; in [18,26,11] a subgradient method is used to attain dual optimality, whereas in [24,20,10,19] a fast gradient method is used. All these methods make use of only the first-order derivatives of the dual function to obtain a search direction and their theoretical and practical convergence can therefore not be faster than sublinear.…”

mentioning

confidence: 99%

Numerical Structure of the Hessian of the Lagrange Dual Function for a Class of Convex Problems

Klintberg¹,

Gros²

2017

SIAM J. Control Optim.

View full text Add to dashboard Cite

Abstract. This paper considers a structured separable convex optimization problem, motivated by the deployment of model predictive control on multiagent systems that are interacting via nondelayed couplings. We show that the dual decomposition of this problem yields a numerical structure in the Hessian of the dual function. This numerical structure allows for deploying a quasiNewton method in the dual space. For large problems, this approach yields a large reduction of the computational complexity of solving the problem, and for geographically distributed problems a reduction in the communication burden.

show abstract

Metric selection in fast dual forward–backward splitting

Giselsson

Boyd

2015

Automatica

View full text Add to dashboard Cite

Improved Dual Decomposition for Distributed Model Predictive Control

Cited by 9 publications

References 15 publications

Preconditioning in fast dual gradient methods

Preconditioning in fast dual gradient methods

Numerical Structure of the Hessian of the Lagrange Dual Function for a Class of Convex Problems

Metric selection in fast dual forward–backward splitting

Contact Info

Product

Resources

About