On the solution of large-scale SDP problems by the modified barrier method using iterative solvers

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Kocvara M, Stingl M
Zeitschrift: Mathematical Programming
Verlag: Springer Verlag (Germany)
Jahr der Veröffentlichung: 2007
Band: 109
Heftnummer: 2
Seitenbereich: 413-444
ISSN: 0025-5610


Abstract


The limiting factors of second-order methods for large-scale semidefinite optimization are the storage and factorization of the Newton matrix. For a particular algorithm based on the modified barrier method, we propose to use iterative solvers instead of the routinely used direct factorization techniques. The preconditioned conjugate gradient method proves to be a viable alternative for problems with a large number of variables and modest size of the constrained matrix. We further propose to avoid explicit calculation of the Newton matrix either by an implicit scheme in the matrix–vector product or using a finite-difference formula. This leads to huge savings in memory requirements and, for certain problems, to further speed-up of the algorithm.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Stingl, Michael Prof. Dr.
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)


Zitierweisen

APA:
Kocvara, M., & Stingl, M. (2007). On the solution of large-scale SDP problems by the modified barrier method using iterative solvers. Mathematical Programming, 109(2), 413-444. https://dx.doi.org/10.1007/s10107-008-0250-9

MLA:
Kocvara, Michal, and Michael Stingl. "On the solution of large-scale SDP problems by the modified barrier method using iterative solvers." Mathematical Programming 109.2 (2007): 413-444.

BibTeX: 

Zuletzt aktualisiert 2018-22-07 um 00:53