On the Central Paths in Symmetric Cone Programming

Héctor Ramírez () and David Sossa ()
Additional contact information
Héctor Ramírez: Universidad de Chile
David Sossa: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 2, No 15, 649-668

Abstract: Abstract This paper is devoted to the study of optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the existence and the convergence of primal, dual and primal–dual central paths. We are then able to establish concrete characterizations of the limit points of these central paths for specific subclasses. Indeed, for the class of barrier functions defined at the origin, we prove that the limit point of a primal central path minimizes the corresponding barrier function over the solution set of the studied symmetric cone program. In addition, we show that the limit points of the primal and dual central paths lie in the relative interior of the primal and dual solution sets for the case of the logarithm and modified logarithm barriers.

Keywords: Symmetric cone programming; Central paths; Barrier functions; Recession functions; Euclidean Jordan algebra; 90C25; 90C51; 17C27 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-016-0989-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:joptap:v:172:y:2017:i:2:d:10.1007_s10957-016-0989-8

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-016-0989-8

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().