A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps

Jia-Wang Nie and Ya-Xiang Yuan ()

Annals of Operations Research, 2001, vol. 103, issue 1, 115-133

Abstract: Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor–corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K 0 , we use Dikin-type step. Otherwise, Newton centering step is taken. In both cases, step-length is determined by line search. We show that at least a constant reduction in the potential function is guaranteed. Moreover the algorithm is proved to terminate in O $$(\sqrt n $$ log (1/ε)) steps. In the end of this paper, we discuss how to compute search direction (ΔX,ΔS) using the conjugate gradient method. Copyright Kluwer Academic Publishers 2001

Keywords: semi-definite programming; quadratic term; potential function; central path; predictor step; corrector step; Dikin-type step; Newton centering step (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1023/A:1012994820412 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:103:y:2001:i:1:p:115-133:10.1023/a:1012994820412

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1023/A:1012994820412

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().