liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
A Distributed Primal-dual Interior-point Method for Loosely Coupled Problems Using ADMM
KTH Royal Institute of Technology. (Automatic Control)
Linköping University, Department of Electrical Engineering, Automatic Control.
Linköping University, Department of Electrical Engineering, Automatic Control.
KTH Royal Institute of Technology. (Automatic Control)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-dual interior-point methods with the remarkable parallelizability of ADMM. The resulting algorithm has superior computational properties with respect to ADMM directly applied to our problem. The amount of computations that needs to be conducted by each computing agent is far less. In particular, the updates for all variables can be expressed in closed form, irrespective of the type of optimization problem. The most expensive computational burden of the algorithm occur in the updates of the primal variables and can be precomputed in each iteration of the interior-point method. We verify and compare our method to ADMM in numerical experiments.

National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-117495OAI: oai:DiVA.org:liu-117495DiVA: diva2:808667
Available from: 2015-04-29 Created: 2015-04-29 Last updated: 2015-05-19
In thesis
1. Divide and Conquer: Distributed Optimization and Robustness Analysis
Open this publication in new window or tab >>Divide and Conquer: Distributed Optimization and Robustness Analysis
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

As control of large-scale complex systems has become more and more prevalent within control, so has the need for analyzing such controlled systems. This is particularly due to the fact that many of the control design approaches tend to neglect intricacies in such systems, e.g., uncertainties, time delays, nonlinearities, so as to simplify the design procedure.

Robustness analysis techniques allow us to assess the effect of such neglected intricacies on performance and stability. Performing robustness analysis commonly requires solving an optimization problem. However, the number of variables of this optimization problem, and hence the computational time, scales badly with the dimension of the system. This limits our ability to analyze large-scale complex systems in a centralized manner. In addition, certain structural constraints, such as privacy requirements or geographical separation, can prevent us from even forming the analysis problem in a centralized manner.

In this thesis, we address these issues by exploiting structures that are common in large-scale systems and/or their corresponding analysis problems. This enables us to reduce the computational cost of solving these problems both in a centralized and distributed manner. In order to facilitate distributed solutions, we employ or design tailored distributed optimization techniques. Particularly, we propose three distributed optimization algorithms for solving the analysis problem, which provide superior convergence and/or computational properties over existing algorithms. Furthermore, these algorithms can also be used for solving general loosely coupled optimization problems that appear in a variety of fields ranging from control, estimation and communication systems to supply chain management and economics.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2015. 330 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1676
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-117503 (URN)10.3384/diss.diva-117503 (DOI)978-91-7519-050-1 (print) (ISBN)
Public defence
2015-06-11, Visionen, Hus B, Campus Valla, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2015-05-04 Created: 2015-04-29 Last updated: 2015-05-19Bibliographically approved

Open Access in DiVA

No full text

Other links

http://arxiv.org/abs/1406.2192

Search in DiVA

By author/editor
Khoshfetrat Pakazad, Sina
By organisation
Automatic Control
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 98 hits
ReferencesLink to record
Permanent link

Direct link