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A Genetic Programming Approach to the Matrix BandwidthMinimization Problem
"... Abstract. The bandwidth of a sparse matrix is the distance from the main diagonal beyond which all elements of the matrix are zero. The bandwidth minimisation problem for a matrix consists of finding the permutation of rows and columns of the matrix which ensures that the nonzero elements are locat ..."
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are located in as narrow a band as possible along the main diagonal. This problem, which is known to be NPcomplete, can also be formulated as a vertex labelling problem for a graph whose edges represent the nonzero elements of the matrix. In this paper, a Genetic Programming approach is proposed and tested
Genetic Programming
, 1997
"... Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring ..."
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Cited by 1056 (12 self)
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Introduction Genetic programming is a domainindependent problemsolving approach in which computer programs are evolved to solve, or approximately solve, problems. Genetic programming is based on the Darwinian principle of reproduction and survival of the fittest and analogs of naturally occurring
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
Robust principal component analysis?
 Journal of the ACM,
, 2011
"... Abstract This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a lowrank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the lowrank and the ..."
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Cited by 569 (26 self)
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rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the 1 norm. This suggests the possibility of a principled approach to robust principal component
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
Adaptive memory programming for matrix bandwidth minimization
 Annals of Operations Research
"... In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a permutati ..."
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Cited by 2 (0 self)
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In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a
FastHenry: A MultipoleAccelerated 3D Inductance Extraction Program
, 1993
"... ... based on mesh analysis can be combined with a GMRESstyle iterative matrix solution technique to make a reasonably fast 3D frequency dependent inductance and resistance extraction algorithm. Unfortunately, both the computation time and memory re quired for that approach grow faster than n 2, w ..."
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Cited by 216 (48 self)
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... based on mesh analysis can be combined with a GMRESstyle iterative matrix solution technique to make a reasonably fast 3D frequency dependent inductance and resistance extraction algorithm. Unfortunately, both the computation time and memory re quired for that approach grow faster than n 2
Benchmarking GPUs to tune dense linear algebra
, 2008
"... We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80–90 % of the pe ..."
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Cited by 242 (2 self)
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We present performance results for dense linear algebra using recent NVIDIA GPUs. Our matrixmatrix multiply routine (GEMM) runs up to 60 % faster than the vendor’s implementation and approaches the peak of hardware capabilities. Our LU, QR and Cholesky factorizations achieve up to 80
Autonomous mental development by robots and animals
"... How does one create an intelligent machine? This problem has proven difficult. Over the past several decades, scientists have taken one of three approaches: In the first, which is knowledgebased, an intelligent machine in a laboratory is directly programmed to perform a given task. In a second, lea ..."
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Cited by 227 (38 self)
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How does one create an intelligent machine? This problem has proven difficult. Over the past several decades, scientists have taken one of three approaches: In the first, which is knowledgebased, an intelligent machine in a laboratory is directly programmed to perform a given task. In a second
A Sparse Signal Reconstruction Perspective for Source Localization With Sensor Arrays
, 2005
"... We present a source localization method based on a sparse representation of sensor measurements with an overcomplete basis composed of samples from the array manifold. We enforce sparsity by imposing penalties based on the 1norm. A number of recent theoretical results on sparsifying properties of ..."
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Cited by 231 (6 self)
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or frequency samples. Our formulation leads to an optimization problem, which we solve efficiently in a secondorder cone (SOC) programming framework by an interior point implementation. We propose a grid refinement method to mitigate the effects of limiting estimates to a grid of spatial locations
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