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2,192
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task
Monopolistic competition and optimum product diversity. The American Economic Review,
, 1977
"... The basic issue concerning production in welfare economics is whether a market solution will yield the socially optimum kinds and quantities of commodities. It is well known that problems can arise for three broad reasons: distributive justice; external effects; and scale economies. This paper is c ..."
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Cited by 1911 (5 self)
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is concerned with the last of these. The basic principle is easily stated.' A commodity should be produced if the costs can be covered by the sum of revenues and a properly defined measure of consumer's surplus. The optimum amount is then found by equating the demand price and the marginal cost
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 365 (5 self)
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and the onenorm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a rootfinding algorithm for finding arbitrary points
On Visibility and Covering By Convex Sets
, 1999
"... A set X ` IR d is nconvex if among any n its points there exist two such that the segment connecting them is contained in X. Perles and Shelah have shown that any closed (n + 1)convex set in the plane is the union of at most n 6 convex sets. We improve their bound to 18n 3 , and show a lower ..."
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Cited by 6 (1 self)
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A set X ` IR d is nconvex if among any n its points there exist two such that the segment connecting them is contained in X. Perles and Shelah have shown that any closed (n + 1)convex set in the plane is the union of at most n 6 convex sets. We improve their bound to 18n 3 , and show a
Logarithmic regret algorithms for online convex optimization
 In 19’th COLT
, 2006
"... Abstract. In an online convex optimization problem a decisionmaker makes a sequence of decisions, i.e., choose a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters an sequence of (possibly unrelated) convex cost functions. Zinkevich [Zin03] i ..."
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Cited by 210 (35 self)
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Abstract. In an online convex optimization problem a decisionmaker makes a sequence of decisions, i.e., choose a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters an sequence of (possibly unrelated) convex cost functions. Zinkevich [Zin03
On the minimum volume covering ellipsoid of ellipsoids
 SIAM Journal on Optimization
, 2006
"... We study the problem of computing a (1+ɛ)approximation to the minimum volume covering ellipsoid of a given set S of the convex hull of m fulldimensional ellipsoids in R n. We extend the firstorder algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellips ..."
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Cited by 16 (2 self)
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provides a good approximation to that of S. Furthermore, the size of X depends only on the dimension n and ɛ, but not on the number of ellipsoids m. We also discuss the extent to which our algorithm can be used to compute the minimum volume covering ellipsoid of the convex hull of other sets in R n. We
Efficient SVM training using lowrank kernel representations
 Journal of Machine Learning Research
, 2001
"... SVM training is a convex optimization problem which scales with the training set size rather than the feature space dimension. While this is usually considered to be a desired quality, in large scale problems it may cause training to be impractical. The common techniques to handle this difficulty ba ..."
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Cited by 240 (3 self)
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SVM training is a convex optimization problem which scales with the training set size rather than the feature space dimension. While this is usually considered to be a desired quality, in large scale problems it may cause training to be impractical. The common techniques to handle this difficulty
Computation of Minimum Volume Covering Ellipsoids
 Operations Research
, 2003
"... We present a practical algorithm for computing the minimum volume ndimensional ellipsoid that must contain m given points a 1 , . . . , am . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structur ..."
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Cited by 35 (0 self)
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We present a practical algorithm for computing the minimum volume ndimensional ellipsoid that must contain m given points a 1 , . . . , am . This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its
Minimum Convex Partition of a Constrained Point Set
 DISCRETE APPLIED MATHEMATICS
, 1998
"... A convex partition with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is a convex polygon. A minimum convex partition with respect to S is a ..."
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Cited by 10 (1 self)
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A convex partition with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and every bounded interior face is a convex polygon. A minimum convex partition with respect
Results 1  10
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2,192