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On Optimal Locality of Linear Relaxation
"... Tiling is wellknown to reduce the number of cache misses in linear relaxation codes. This paper investigates analytically how close to optimum the improvement gets. We consider one time step of the Jacobi and GaussSeidel methods on a twodimensional array of size (N +2) (N +2). For cache capaci ..."
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Cited by 1 (0 self)
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Tiling is wellknown to reduce the number of cache misses in linear relaxation codes. This paper investigates analytically how close to optimum the improvement gets. We consider one time step of the Jacobi and GaussSeidel methods on a twodimensional array of size (N +2) (N +2). For cache
Validated Probing with Linear Relaxations
"... Abstract. During branch and bound search in deterministic global optimization, adaptive subdivision is used to produce subregions x, which are then eliminated, shown to contain an optimal point, reduced in size, or further subdivided. The various techniques used to reduce or eliminate a subregion x ..."
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determine the efficiency and practicality of the algorithm. Ryoo and Sahinidis have proposed a “probing” technique, involving the dual variables of a linear relaxation, to reduce the size of subregions x. This technique, combined with others, has been successful in the BARON global optimization software
Rigorous filtering using linear relaxations
, 2010
"... This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set o ..."
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Cited by 5 (3 self)
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This paper presents rigorous filtering methods for continuous constraint satisfaction problems based on linear relaxations. Filtering or pruning stands for reducing the search space of constraint satisfaction problems. Discussed are old and new approaches for rigorously enclosing the solution set
On linear relaxations of OPF problems
"... . The AC OPF problem is a fundamental software component in the operation of electrical power transmission systems. For background, see [1]. It can be formulated as a nonconvex, continuous optimization problem. In routine problem instances, solutions of excellent quality can be quickly obtained usi ..."
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. The AC OPF problem is a fundamental software component in the operation of electrical power transmission systems. For background, see [1]. It can be formulated as a nonconvex, continuous optimization problem. In routine problem instances, solutions of excellent quality can be quickly obtained using a variety of methodologies, including sequential lin
Linear relaxations for transmission system planning
 IEEE Transactions on Power Systems
, 2011
"... We apply a linear relaxation procedure for polynomial optimization problems to transmission system planning. The approach recovers and improves upon existing linear models based on the DC approximation. We then consider the full AC problem, and obtain new linear models with nearly the same efficien ..."
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Cited by 6 (1 self)
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We apply a linear relaxation procedure for polynomial optimization problems to transmission system planning. The approach recovers and improves upon existing linear models based on the DC approximation. We then consider the full AC problem, and obtain new linear models with nearly the same
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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that convex relaxation succeeds. As evidence of the broad impact of these results, the paper describes how convex relaxation can be used for several concrete signal recovery problems. It also describes applications to channel coding, linear regression, and numerical analysis.
A Linear Relaxation Heuristic For The Generalized Assignment Problem
 Naval Research Logistics
, 1992
"... We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where t ..."
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Cited by 17 (1 self)
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We examine the basis structure of the linear relaxation of the generalized assignment problem. The basis gives a surprising amount of information. This leads to a very simple heuristic that uses only generalized network optimization codes. Lower bounds can be generated by cut generation, where
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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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
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
Linear spatial pyramid matching using sparse coding for image classification
 in IEEE Conference on Computer Vision and Pattern Recognition(CVPR
, 2009
"... Recently SVMs using spatial pyramid matching (SPM) kernel have been highly successful in image classification. Despite its popularity, these nonlinear SVMs have a complexity O(n 2 ∼ n 3) in training and O(n) in testing, where n is the training size, implying that it is nontrivial to scaleup the algo ..."
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Cited by 488 (19 self)
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the algorithms to handle more than thousands of training images. In this paper we develop an extension of the SPM method, by generalizing vector quantization to sparse coding followed by multiscale spatial max pooling, and propose a linear SPM kernel based on SIFT sparse codes. This new approach remarkably
Results 1  10
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444,442