SIAM Journal on Scientific Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
SIAM Review
An exact duality theory for semidefinite programming and its complexity implications
Mathematical Programming: Series A and B
A Graph Based Method for Generating the Fiedler Vector of Irregular Problems
Proceedings of the 11 IPPS/SPDP'99 Workshops Held in Conjunction with the 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing
A Multilevel Algorithm for Spectral Partitioning with Extended Eigen-Models
IPDPS '00 Proceedings of the 15 IPDPS 2000 Workshops on Parallel and Distributed Processing
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
Semidefinite programming for graph partitioning with preferences in data distribution
VECPAR'02 Proceedings of the 5th international conference on High performance computing for computational science
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A semidefinite program (SDP) is an optimization problem over n 脳 n symmetric matrices where a linear function of the entries is to be minimized subject to linear equality constraints, and the condition that the unknown matrix is positive semidefinite. Standard techniques for solving SDP's require O(n3) operations per iteration. We introduce subspace algorithms that greatly reduce the cost os solving large-scale SDP's. We apply these algorithms to SDP approximations of graph partitioning problems. We numerically compare our new algorithm with a standard semidefinite programming algorithm and show that our subspace algorithm performs better.