1,427 research outputs found
On the Burer-Monteiro method for general semidefinite programs
Consider a semidefinite program (SDP) involving an positive
semidefinite matrix . The Burer-Monteiro method uses the substitution to obtain a nonconvex optimization problem in terms of an
matrix . Boumal et al. showed that this nonconvex method provably solves
equality-constrained SDPs with a generic cost matrix when , where is the number of constraints. In this note we extend
their result to arbitrary SDPs, possibly involving inequalities or multiple
semidefinite constraints. We derive similar guarantees for a fixed cost matrix
and generic constraints. We illustrate applications to matrix sensing and
integer quadratic minimization.Comment: 10 page
Approximate Rank-Detecting Factorization of Low-Rank Tensors
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3
tensor and calculates its factorization into rank-one components. We provide
generative conditions for the algorithm to work and demonstrate on both
synthetic and real world data that AROFAC2 is a potentially outperforming
alternative to the gold standard PARAFAC over which it has the advantages that
it can intrinsically detect the true rank, avoids spurious components, and is
stable with respect to outliers and non-Gaussian noise
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