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Ssemigoodness for LowRank Semidefinite Matrix Recovery
"... Abstract We extend and characterize the concept of ssemigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in lowrank semidefinite matrix recovery. We show that ssemigoodness is not only a ..."
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Abstract We extend and characterize the concept of ssemigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in lowrank semidefinite matrix recovery. We show that ssemigoodness is not only a
A New Algorithm for Positive Semidefinite Matrix Completion
"... Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and lowrank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm regularized ..."
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Positive semidefinite matrix completion (PSDMC) aims to recover positive semidefinite and lowrank matrices from a subset of entries of a matrix. It is widely applicable in many fields, such as statistic analysis and system control. This task can be conducted by solving the nuclear norm
Positive semidefinite matrix completions on chordal graphs and the constraint nondegeneracy in semidefinite programming
, 2008
"... LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint n ..."
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Cited by 4 (0 self)
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LetG = (V,E) be a graph. In matrix completion theory, it is known that the following two conditions are equivalent: (i) G is a chordal graph; (ii) Every Gpartial positive semidefinite matrix has a positive semidefinite matrix completion. In this paper, we relate these two conditions to constraint
ZONAL POLYNOMIALS OF POSITIVE SEMIDEFINITE MATRIX ARGUMENT
, 2004
"... By using the linear structure theory of Magnus (12), this work proposes an alternative way to James (11) for obtaining the LaplaceBeltrami operator, who has the zonal polynomials of positive definite matrix argument as eigenfunctions, in particular, an explicit expression for the matrix G(v(X)), ..."
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theory of James (11) a differential metric depending on the MoorePenrose inverse is proposed for the space of m×m positive semidefinite matrices. As in the definite case, the LaplaceBeltrami operator for the calculation of zonal polynomials of positive semidefinite matrix argument is derived. In a
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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problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
Error Bounds for Eigenvalue and Semidefinite Matrix Inequality Systems
"... Dedicated to Terry Rockafellar in honor of his 70th birthday Received: date / Revised version: date Abstract. In this paper we give sufficient conditions for existence of error bounds for systems expressed in terms of eigenvalue functions (such as in eigenvalue optimization) or positive semidefinite ..."
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Cited by 2 (0 self)
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semidefiniteness (such as in semidefinite programming). 1.
Complexity of the positive semidefinite matrix completion problem with a rank constraint
, 2014
"... We consider the decision problem asking whether a partial rational symmetric matrix with an allones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NPhard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NPhard to test me ..."
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Cited by 3 (3 self)
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We consider the decision problem asking whether a partial rational symmetric matrix with an allones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NPhard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NPhard to test
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
Positive Semidefinite Matrix Completion, Universal Rigidity and the Strong Arnold Property
, 2013
"... This paper addresses the following three topics: positive semidefinite (psd) matrix completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We show some strong connections among these topics, using semidefinite programming as unifying theme. Our main contribution is a su ..."
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Cited by 4 (1 self)
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This paper addresses the following three topics: positive semidefinite (psd) matrix completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We show some strong connections among these topics, using semidefinite programming as unifying theme. Our main contribution is a
Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
, 2009
"... We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of th ..."
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We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image
Results 1  10
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