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Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 775 (21 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized
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 254 (19 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
Semidefinite optimization
 Acta Numerica
, 2001
"... Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the ..."
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Cited by 152 (2 self)
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Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
, 2001
"... Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) constraints. Except in some special cases, solving this rank minimization probiem (globally) is ve ..."
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Cited by 274 (10 self)
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) is very difficult. One simple and surprisingly effective heuristic, applicable when the matrix variable is symmetric and positive semidefinite, is to minimize its trace in place of its rank. This results in a semidefinite program (SDP) which can be efficiently solved. In this paper we describe a
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
 SIAM JOURNAL ON OPTIMIZATION
, 1999
"... A critical disadvantage of primaldual interiorpoint methods against dual interiorpoint methods for large scale SDPs (semidefinite programs) has been that the primal positive semidefinite variable matrix becomes fully dense in general even when all data matrices are sparse. Based on some fundamenta ..."
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Cited by 102 (31 self)
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A critical disadvantage of primaldual interiorpoint methods against dual interiorpoint methods for large scale SDPs (semidefinite programs) has been that the primal positive semidefinite variable matrix becomes fully dense in general even when all data matrices are sparse. Based on some
Analysis of the Cholesky decomposition of a semidefinite matrix
 in Reliable Numerical Computation
, 1990
"... Perturbation theory is developed for the Cholesky decomposition of an n × n symmetric positive semidefinite matrix A of rank r. The matrix W = A −1 11 A12 is found to play a key role in the perturbation bounds, where A11 and A12 are r × r and r × (n − r) submatrices of A respectively. A backward er ..."
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Cited by 65 (4 self)
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Perturbation theory is developed for the Cholesky decomposition of an n × n symmetric positive semidefinite matrix A of rank r. The matrix W = A −1 11 A12 is found to play a key role in the perturbation bounds, where A11 and A12 are r × r and r × (n − r) submatrices of A respectively. A backward
Binary Positive Semidefinite Matrices and Associated Integer Polytopes
"... We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and wellknown integer polytopes — the cut, boolean quadric, ..."
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Cited by 3 (0 self)
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We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and wellknown integer polytopes — the cut, boolean quadric
Positive semidefinite rank
, 2014
"... Let M ∈ Rp×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices Ai, Bj of size k × k such that Mij = trace(AiBj). The psd rank has many appealing geometric interpretations, including semidefinite re ..."
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Cited by 6 (0 self)
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Let M ∈ Rp×q be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices Ai, Bj of size k × k such that Mij = trace(AiBj). The psd rank has many appealing geometric interpretations, including semidefinite
Robust Binary Image Deconvolution with Positive Semidefinite Programming
"... This paper reports on a novel approach to binary image deconvolution using Positive Semidefinite (PSD) Programming. We note the combinatorial nature of this problem: binary image deconvolution requires the minimization of a global energy function over binary variables, taking into account not only b ..."
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This paper reports on a novel approach to binary image deconvolution using Positive Semidefinite (PSD) Programming. We note the combinatorial nature of this problem: binary image deconvolution requires the minimization of a global energy function over binary variables, taking into account not only
Results 1  10
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