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An InteriorPoint Method for Semidefinite Programming
, 2005
"... We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other appli ..."
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Cited by 255 (18 self)
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We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices. We show that the approach is very efficient for graph bisection problems, such as maxcut. Other applications include maxmin eigenvalue problems and relaxations for the stable set problem.
A Spectral Approach to Bandwidth and Separator Problems in Graphs
, 1993
"... Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the i ..."
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Cited by 16 (5 self)
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Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The bounds are based on a projection technique developed for the quadratic assignment problem, and once more demonstrate the importance of the extreme eigenvalues of the Laplacian. They will be shown to be strict for certain classes of graphs and compare favourably to bounds already known in literature. Further improvement is gained by applying nonlinear optimization methods.