TY - JOUR
T1 - Max-min eigenvalue problems, primal-dual interior point algorithms, and trust region subproblems
AU - Rendl, Franz
AU - Vanderbei, Robert J.
AU - Wolkowicz, Henry
N1 - Funding Information:
v ~ h ipsaper was presented at the NATO Advanced Study Institute on Algorithms for Continuous Optimization, n Ciocco, Italy, September, 1993. *Research support by Christian Doppler Laboratorium fiir Dislcrete Optimierung. +Research support by AFOSR through grant AFOSR-91-0359. $Research support by the National Science and Engineering Research Council Canada.
PY - 1995/1/1
Y1 - 1995/1/1
N2 - 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 problem to one with constraints over the cone of positive semidefinite matrices, i.e. Löwner order constraints. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row.
AB - 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 problem to one with constraints over the cone of positive semidefinite matrices, i.e. Löwner order constraints. One of the algorithms does this transformation through an intermediate transformation to a trust region subproblem. This allows the removal of a dense row.
KW - 1 programming
KW - Graph bisection
KW - Löwner partial order
KW - Max-min eigenvalue problems
KW - Primal-dual interior point methods
KW - Quadratic 0
KW - Trust region subproblems
UR - http://www.scopus.com/inward/record.url?scp=0029425729&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0029425729&partnerID=8YFLogxK
U2 - 10.1080/10556789508805599
DO - 10.1080/10556789508805599
M3 - Article
AN - SCOPUS:0029425729
SN - 1055-6788
VL - 5
SP - 1
EP - 16
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 1
ER -