On the local convergence of a predictor-corrector method for semidefinite programming

Citation
J. Ji et al., On the local convergence of a predictor-corrector method for semidefinite programming, SIAM J OPTI, 10(1), 1999, pp. 195-210
Citations number
17
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON OPTIMIZATION
ISSN journal
10526234 → ACNP
Volume
10
Issue
1
Year of publication
1999
Pages
195 - 210
Database
ISI
SICI code
1052-6234(19991129)10:1<195:OTLCOA>2.0.ZU;2-Y
Abstract
We study the local convergence of a predictor-corrector algorithm for semid efinite programming problems based on the Monteiro-Zhang unified direction whose polynomial convergence was recently established by Monteiro. Under st rict complementarity and nondegeneracy assumptions superlinear convergence with Q-order 1.5 is proved if the scaling matrices in the corrector step ha ve bounded condition number. A version of the predictor-corrector algorithm enjoys quadratic convergence if the scaling matrices in both predictor and corrector steps have bounded condition numbers. The latter results apply i n particular to algorithms using the Alizadeh-Haeberly-Overton (AHO) direct ion since there the scaling matrix is the identity matrix.