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328,599
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
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
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 711 (0 self)
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is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation
A characterization of convex problems in decentralized control
 IEEE Transactions on Automatic Control
"... Abstract—We consider the problem of constructing optimal decentralized controllers. We formulate this problem as one of minimizing the closedloop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set with respe ..."
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Cited by 126 (24 self)
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with respect to a system, and show that if the constraint set has this property, then the constrained minimumnorm problem may be solved via convex programming. We also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. These results are developed
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 860 (27 self)
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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
Primaldual subgradient methods for convex problems
, 2005
"... (after revision) In this paper we present a new approach for constructing subgradient schemes for different types of nonsmooth problems with convex structure. Our methods are primaldual since they are always able to generate a feasible approximation to the optimum of an appropriately formulated dual ..."
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Cited by 144 (3 self)
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(after revision) In this paper we present a new approach for constructing subgradient schemes for different types of nonsmooth problems with convex structure. Our methods are primaldual since they are always able to generate a feasible approximation to the optimum of an appropriately formulated
Convex Position Estimation in Wireless Sensor Networks
"... A method for estimating unknown node positions in a sensor network based exclusively on connectivityinduced constraints is described. Known peertopeer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem fo ..."
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Cited by 491 (0 self)
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A method for estimating unknown node positions in a sensor network based exclusively on connectivityinduced constraints is described. Known peertopeer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem
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.
Homogeneous penalizers and constraints in convex problems
, 2012
"... This is an extended version of section 3 of the paper “Homogeneous penalizers and constraints in convex problems ” written by R. Ciak, B. Shafei and G. Steidl Acknowledgements I like to acknowledge my advisor for her help. In particular I like to say thanks for the introduction written almost compl ..."
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Cited by 1 (0 self)
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This is an extended version of section 3 of the paper “Homogeneous penalizers and constraints in convex problems ” written by R. Ciak, B. Shafei and G. Steidl Acknowledgements I like to acknowledge my advisor for her help. In particular I like to say thanks for the introduction written almost
Results 1  10
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328,599