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Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 568 (23 self)
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for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds
COMPUTATIONAL COMPLEXITY OF TENSOR NUCLEAR NORM
"... Abstract. The main result of this paper is that the weak membership problem in the unit ball of a given norm is NPhard if and only if the weak membership problem in the unit ball of the dual norm is NPhard. Equivalently, the approximation of a given norm is polynomial time if and only if the appro ..."
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if the approximation of the dual norm is polynomial time. Using the NPhardness of the approximation of spectral norm of tensors we prove that the approximation of nuclear norm of tensors is NPhard. In addition, we show that bipartite separability of a density matrix is equivalent its corresponding 4tensor having
Reweighted nuclear norm minimization with application to system identification
 Proc. American Control Conference
, 2010
"... Abstractâ€”The matrix rank minimization problem consists of finding a matrix of minimum rank that satisfies given convex constraints. It is NPhard in general and has applications in control, system identification, and machine learning. Reweighted trace minimization has been considered as an iterative ..."
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Cited by 26 (4 self)
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as an iterative heuristic for this problem. In this paper, we analyze the convergence of this iterative heuristic, showing that the difference between successive iterates tends to zero. Then, after reformulating the heuristic as reweighted nuclear norm minimization, we propose an efficient gradient
A Simple Algorithm for Nuclear Norm Regularized Problems
"... Optimization problems with a nuclear norm regularization, such as e.g. low norm matrix factorizations, have seen many applications recently. We propose a new approximation algorithm building upon the recent sparse approximate SDP solver of (Hazan, 2008). The experimental efficiency of our method is ..."
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Cited by 48 (3 self)
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Optimization problems with a nuclear norm regularization, such as e.g. low norm matrix factorizations, have seen many applications recently. We propose a new approximation algorithm building upon the recent sparse approximate SDP solver of (Hazan, 2008). The experimental efficiency of our method
Interference alignment using reweighted nuclear norm minimization
 in IEEE Int. Conf. Acoust., Speech Signal Process
, 2013
"... This paper proposes an algorithm to compute the transmit beamformers for linear interference alignment for the MIMO interference channel and the MIMO interfering multipleaccess/broadcast channel without symbol extensions. We first formulate the interference alignment problem as a rank minimization p ..."
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Cited by 3 (3 self)
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problem with linear constraints, then approximate the matrix rank by the nuclear norm. We further propose the use of an iterative reweighted nuclear norm approach and show that adaptive reweighting can significantly improve the algorithmâ€™s ability to find aligned beamformers. Simulation results show
Nuclear normregularized SENSE reconstruction
 Magnetic Reson Imaging
, 2012
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 4 (0 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
A Weighted Nuclear Norm Method for Tensor Completion
"... In recent years, tensor completion problem has received a significant amount of attention in computer vision, data mining and neuroscience. It is the higher order generalization of matrix completion. And these can be solved by the convex relaxation which minimizes the tensor nuclear norm instead of ..."
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In recent years, tensor completion problem has received a significant amount of attention in computer vision, data mining and neuroscience. It is the higher order generalization of matrix completion. And these can be solved by the convex relaxation which minimizes the tensor nuclear norm instead
An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems
, 2009
"... ..."
Weighted Nuclear Norm Minimization with Application to Image Denoising
"... As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. Howe ..."
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Cited by 5 (2 self)
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As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function
Results 1  10
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71,434