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81,019
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 483 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Convex programming methods for global optimization
 in COCOS
, 2003
"... Abstract. We investigate some approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. We assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We pro ..."
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Cited by 3 (1 self)
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Abstract. We investigate some approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. We assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We
Just relax: Convex programming methods for subset selection and sparse approximation
, 2004
"... Subset selection and sparse approximation problems request a good approximation of an input signal using a linear combination of elementary signals, yet they stipulate that the approximation may only involve a few of the elementary signals. This class of problems arises throughout electrical enginee ..."
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Cited by 103 (5 self)
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. This report demonstrates that the solution of the convex program frequently coincides with the solution of the original approximation problem. The proofs depend essentially on geometric properties of the ensemble of elementary signals. The results are powerful because sparse approximation problems
A Nonnnegatively Constrained Convex Programming Method for Image Reconstruction
 SIAM Journal on Scientific Computing
"... Abstract. We consider a largescale convex minimization problem with nonnegativity constraints that arises in astronomical imaging. We develop a cost functional which incorporates the statistics of the noise in the image data and Tikhonov regularization to induce stability. We introduce an efficien ..."
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Cited by 27 (15 self)
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Abstract. We consider a largescale convex minimization problem with nonnegativity constraints that arises in astronomical imaging. We develop a cost functional which incorporates the statistics of the noise in the image data and Tikhonov regularization to induce stability. We introduce
Sequential convex programming methods for a class of structured nonlinear programming
"... In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the firstorder optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a co ..."
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Cited by 6 (1 self)
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In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the firstorder optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a
Efficient decoupling capacitor planning via convex programming methods
 Proc. Int. Symp. Phy
, 2006
"... Achieving power/ground (P/G) supply signal integrity is crucial to success of nanometer VLSI designs. Existing P/G network optimization techniques are dominated by sensitivity based approaches. In this paper, we propose two novel convex programming based approaches for decoupling capacitor insertion ..."
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Cited by 2 (0 self)
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Achieving power/ground (P/G) supply signal integrity is crucial to success of nanometer VLSI designs. Existing P/G network optimization techniques are dominated by sensitivity based approaches. In this paper, we propose two novel convex programming based approaches for decoupling capacitor
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
, 2011
"... ..."
Interiorpoint Methods
, 2000
"... The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadrati ..."
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Cited by 612 (15 self)
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The modern era of interiorpoint methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex
Robust convex optimization
 Mathematics of Operations Research
, 1998
"... We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U. The ensuing optimization problem is called robust optimization. In this paper we la ..."
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Cited by 416 (21 self)
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) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficient algorithms such as polynomial time interior point methods.
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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by solving a simple convex optimization program. This program finds the matrix with minimum nuclear norm that fits the data. The condition above assumes that the rank is not too large. However, if one replaces the 1.2 exponent with 1.25, then the result holds for all values of the rank. Similar results hold
Results 1  10
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