Loading…
Bounds on Eigenvalues of Matrices Arising from Interior-Point Methods
Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequence of linear systems that typically become increasingly ill-conditioned with the iterations. To solve these systems, whose original form has a no...
Saved in:
Published in: | SIAM journal on optimization 2014-01, Vol.24 (1), p.49-83 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequence of linear systems that typically become increasingly ill-conditioned with the iterations. To solve these systems, whose original form has a nonsymmetric $3\times 3$ block structure, it is common practice to perform block elimination and either solve the resulting reduced saddle-point system, or further reduce the system to the Schur complement and apply a symmetric positive definite solver. In this paper we use energy estimates to obtain bounds on the eigenvalues of the matrices, and conclude that the original unreduced matrix has more favorable eigenvalue bounds than the alternative reduced versions. Our analysis includes regularized variants of those matrices that do not require typical regularity assumptions. [PUBLICATION ABSTRACT] |
---|---|
ISSN: | 1052-6234 1095-7189 |
DOI: | 10.1137/120890600 |