Max-Min Eigenvalue Problems, Primal-Dual Interior Point Algorithms, and Trust Region Subproblems (1993)
| Venue: | Optimization Methods and Software |
| Citations: | 10 - 4 self |
BibTeX
@ARTICLE{Rendl93max-mineigenvalue,
author = {Franz Rendl and Robert J. Vanderbei and Henry Wolkowicz},
title = {Max-Min Eigenvalue Problems, Primal-Dual Interior Point Algorithms, and Trust Region Subproblems},
journal = {Optimization Methods and Software},
year = {1993},
volume = {5}
}
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Abstract
Two Primal-dual interior point algorithms are presented for the problem of maximizing the smallest eigenvalue of a symmetric matrix over diagonal perturbations. These algorithms prove to be simple, robust, and efficient. Both algorithms are based on transforming the Technische Universitat Graz, Institut fur Mathematik, Kopernikusgasse 24, A-8010 Graz, Austria. Research support by Christian Doppler Laboratorium fur Diskrete Optimierung. y Program in Statistics & Operations Research, Princeton University, Princeton, NJ 08544. Research support by AFOSR through grant AFOSR-91-0359. z Research support by the National Science and Engineering Research Council Canada. problem to one over the cone of positive semidefinite matrices. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row. Key words: Max-min eigenvalue problems, trust region subproblems, Loewner partial order, primal-dual ...
