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243,057
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 780 (22 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
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
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 557 (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
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted LowRank Matrices
, 2009
"... ..."
Flexible smoothing with Bsplines and penalties
 STATISTICAL SCIENCE
, 1996
"... Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots ..."
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Cited by 396 (6 self)
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splines and propose various criteria for the choice of an optimal penalty parameter. Nonparametric logistic regression, density estimation and scatterplot smoothing are used as examples. Some details of the computations are presented.
LOWRANK OPTIMIZATION ON THE CONE OF POSITIVE SEMIDEFINITE MATRICES ∗
"... Abstract. We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = YYT, where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X ..."
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Cited by 28 (6 self)
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X. It is thus very effective for solving problems that have a lowrank solution. The factorization X = YYT leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second
Local minima and convergence in lowrank semidefinite programming
 Mathematical Programming
, 2003
"... The lowrank semidefinite programming problem (LRSDPr) is a restriction of the semidefinite programming problem (SDP) in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr and ..."
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Cited by 44 (2 self)
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The lowrank semidefinite programming problem (LRSDPr) is a restriction of the semidefinite programming problem (SDP) in which a bound r is imposed on the rank of X, and it is well known that LRSDPr is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDPr
Lowrank optimization for semidefinite convex problems ∗
, 807
"... Compiled on July 28, 2008, 12:05 We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable X. This algorithm rests on the factorization X = Y Y T, where the number of columns of Y fixes the rank of X. It is thus very effective ..."
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Cited by 12 (8 self)
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effective for solving programs that have a low rank solution. The factorization X = Y Y T evokes a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second order optimization method
LOWRANK OPTIMIZATION WITH TRACE NORM PENALTY∗
"... Abstract. The paper addresses the problem of lowrank trace norm minimization. We propose an algorithm that alternates between fixedrank optimization and rankone updates. The fixedrank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the sear ..."
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Cited by 18 (5 self)
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Abstract. The paper addresses the problem of lowrank trace norm minimization. We propose an algorithm that alternates between fixedrank optimization and rankone updates. The fixedrank optimization is characterized by an efficient factorization that makes the trace norm differentiable
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
Results 1  10
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243,057