Solving SDP's in Non-commutative Algebras Part I: The Dual-Scaling Algorithm
AbstractSemidefinite programming (SDP) may be viewed as an extension of linear programming (LP), and most interior point methods (IPM s) for LP can be extended to solve SDP problems.However, it is far more difficult to exploit data structures (especially sparsity) in the SDP case.In this paper we will look at the data structure where the SDP data matrices lie in a low dimensional matrix algebra.This data structure occurs in several applications, including the lower bounding of the stability number in certain graphs and the crossing number in complete bipartite graphs.We will show that one can reduce the linear algebra involved in an iteration of an IPM to involve matrices of the size of the dimension of the matrix algebra only.In other words, the original sizes of the data matrices do not appear in the computational complexity bound.In particular, we will work out the details for the dual scaling algorithm, since a dual method is most suitable for the types of applications we have in mind.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2005-17.
Date of creation: 2005
Date of revision:
Contact details of provider:
Web page: http://center.uvt.nl
semidefinite programming; matrix algebras; dual scaling algorithm; exploiting data structure;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- GOEMANS, Michel & RENDL, Franz, 1999. "Semidefinite programs and association schemes," CORE Discussion Papers 1999062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Klerk, E. de, 1997. "Interior point methods for semidefinite programming," Open Access publications from Tilburg University urn:nbn:nl:ui:12-226108, Tilburg University.
- repec:fth:louvco:9962 is not listed on IDEAS
- Klerk, E. de & Pasechnik, D.V., 2005. "A Note on the Stability Number of an Orthogonality Graph," Discussion Paper 2005-66, Tilburg University, Center for Economic Research.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Richard Broekman).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.