Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10957-004-5150-4
Title: Analytic center cutting-plane method with deep cuts for semidefinite feasibility problems
Authors: Chua, S.K. 
Toh, K.C. 
Zhao, G.Y. 
Keywords: Analytic centers
cutting-plane methods
deep cuts
semidefinite feasibility problems
Issue Date: Nov-2004
Citation: Chua, S.K., Toh, K.C., Zhao, G.Y. (2004-11). Analytic center cutting-plane method with deep cuts for semidefinite feasibility problems. Journal of Optimization Theory and Applications 123 (2) : 291-318. ScholarBank@NUS Repository. https://doi.org/10.1007/s10957-004-5150-4
Abstract: An analytic center cutting-plane method with deep cuts for semidefinite feasibility problems is presented. Our objective in these problems is to find a point in a nonempty bounded convex set Γ in the cone of symmetric positive-semidefinite matrices. The cutting plane method achieves this by the following iterative scheme. At each iteration, a query point Ŷ that is an approximate analytic center of the current working set is chosen. We assume that there exists an oracle which either confirms that Ŷ ∈ Γ or returns a cut A ∈ S m such that {Y ∈ S m: A• Y ≤ A• Ŷ - ξ} ⊃Γ, where ξ ≥ 0. Ŷ ∉ Γ, an approximate analytic center of the new working set, defined by adding the new cut to the preceding working set, is then computed via a primal Newton procedure. Assuming that Γ contains a ball with radius ε > 0, the algorithm obtains eventually a point in Γ, with a worst-case complexity of O*(m 3/ε 2) on the total number of cuts generated.
Source Title: Journal of Optimization Theory and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/102860
ISSN: 00223239
DOI: 10.1007/s10957-004-5150-4
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

8
checked on Aug 14, 2018

WEB OF SCIENCETM
Citations

8
checked on Aug 6, 2018

Page view(s)

28
checked on Jun 1, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.