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Local linear convergence for alternating and averaged nonconvex projections
 Found. Comput. Math. 9
"... Key words: alternating projections, averaged projections, linear convergence, metric regularity, distance to illposedness, variational analysis, nonconvexity, extremal principle, proxregularity AMS 2000 Subject Classification: 49M20, 65K10, 90C30 The idea of a finite collection of closed sets havi ..."
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Cited by 43 (10 self)
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Key words: alternating projections, averaged projections, linear convergence, metric regularity, distance to illposedness, variational analysis, nonconvexity, extremal principle, proxregularity AMS 2000 Subject Classification: 49M20, 65K10, 90C30 The idea of a finite collection of closed sets
Evaluating the Accuracy of SamplingBased Approaches to the Calculation of Posterior Moments
 IN BAYESIAN STATISTICS
, 1992
"... Data augmentation and Gibbs sampling are two closely related, samplingbased approaches to the calculation of posterior moments. The fact that each produces a sample whose constituents are neither independent nor identically distributed complicates the assessment of convergence and numerical accurac ..."
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Cited by 604 (12 self)
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accuracy of the approximations to the expected value of functions of interest under the posterior. In this paper methods from spectral analysis are used to evaluate numerical accuracy formally and construct diagnostics for convergence. These methods are illustrated in the normal linear model
On the linear convergence of the ADMM in decentralized consensus optimization
 IEEE Transactions on Signal Processing
, 2014
"... Abstractâ€”In decentralized consensus optimization, a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable, where their information exchange is restricted between the neighbors. To this end, one can first obtain a problem refor ..."
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Cited by 12 (3 self)
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reformulation and then apply the alternating direction method of multipliers (ADMM). The method applies iterative computation at the individual agents and information exchange between the neighbors. This approach has been observed to converge quickly and deemed powerful. This paper establishes its linear
A fast iterative shrinkagethresholding algorithm with application to . . .
, 2009
"... We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast Iterat ..."
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Cited by 1058 (9 self)
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We consider the class of Iterative ShrinkageThresholding Algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods is attractive due to its simplicity, however, they are also known to converge quite slowly. In this paper we present a Fast
The algorithmic analysis of hybrid systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a general framework for the formal specification and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamica ..."
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Cited by 778 (71 self)
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to dynamical laws. For verification purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewiselinear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted
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 547 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
LOCAL LINEAR CONVERGENCE OF ISTA AND FISTA ON THE LASSO PROBLEM âˆ—
"... Abstract. We establish local linear convergence bounds for the ISTA and FISTA iterations on the model LASSO problem. We show that FISTA can be viewed as an accelerated ISTA process. Using a spectral analysis, we show that, when close enough to the solution, both iterations converge linearly, but FIS ..."
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Abstract. We establish local linear convergence bounds for the ISTA and FISTA iterations on the model LASSO problem. We show that FISTA can be viewed as an accelerated ISTA process. Using a spectral analysis, we show that, when close enough to the solution, both iterations converge linearly
Linear Convergence of ADMM on a Model Problem
"... In this short report, we analyze the convergence of ADMM as a matrix recurrence for the particular case of a quadratic program or a linear program. We identify a particular combination of the vector iterates in the standard ADMM iteration that exhibits monotonic convergence. We present an analysis w ..."
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Cited by 5 (0 self)
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In this short report, we analyze the convergence of ADMM as a matrix recurrence for the particular case of a quadratic program or a linear program. We identify a particular combination of the vector iterates in the standard ADMM iteration that exhibits monotonic convergence. We present an analysis
LINEAR CONVERGENCE IN THE APPROXIMATION OF RANKONE CONVEX ENVELOPES
"... Abstract. A linearly convergent iterative algorithm that approximates the rank1 convex envelope f rc of a given function f: Rnm! R, i.e. the largest function below f which is convex along all rank1 lines, is established. The proposed algorithm is a modied version of an approximation scheme due t ..."
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Abstract. A linearly convergent iterative algorithm that approximates the rank1 convex envelope f rc of a given function f: Rnm! R, i.e. the largest function below f which is convex along all rank1 lines, is established. The proposed algorithm is a modied version of an approximation scheme due
Fast linear iterations for distributed averaging.
 Systems & Control Letters,
, 2004
"... Abstract We consider the problem of finding a linear iteration that yields distributed averaging consensus over a network, i.e., that asymptotically computes the average of some initial values given at the nodes. When the iteration is assumed symmetric, the problem of finding the fastest converging ..."
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Cited by 433 (12 self)
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converging linear iteration can be cast as a semidefinite program, and therefore efficiently and globally solved. These optimal linear iterations are often substantially faster than several common heuristics that are based on the Laplacian of the associated graph. We show how problem structure can
Results 11  20
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12,316