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Numerical solution of saddle point problems
 ACTA NUMERICA
, 2005
"... Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has b ..."
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Cited by 322 (25 self)
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Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has
ATOMIC DECOMPOSITION BY BASIS PURSUIT
, 1995
"... The TimeFrequency and TimeScale communities have recently developed a large number of overcomplete waveform dictionaries  stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for d ..."
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Cited by 2728 (61 self)
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successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primaldual logarithmic barrier method and conjugategradient solver.
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 436 (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
Czech Academy of Sciences, Prague,
"... 4 Pavel Jiránek, Miroslav Rozložńık Inexact saddle point solvers and their limiting accuracy Saddle point problems We consider a saddle point problem with the symmetric 2 × 2 block form„ ..."
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4 Pavel Jiránek, Miroslav Rozložńık Inexact saddle point solvers and their limiting accuracy Saddle point problems We consider a saddle point problem with the symmetric 2 × 2 block form„
Preconditioning stochastic Galerkin saddle point systems
 SIAM J. MATRIX ANAL. APPL
, 2009
"... Mixed finite element discretizations of deterministic secondorder elliptic partial differential equations (PDEs) lead to saddle point systems for which the study of iterative solvers and preconditioners is mature. Galerkin approximation of solutions of stochastic secondorder elliptic PDEs, which ..."
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Cited by 110 (4 self)
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Mixed finite element discretizations of deterministic secondorder elliptic partial differential equations (PDEs) lead to saddle point systems for which the study of iterative solvers and preconditioners is mature. Galerkin approximation of solutions of stochastic secondorder elliptic PDEs
The PATH Solver: A NonMonotone Stabilization Scheme for Mixed Complementarity Problems
 OPTIMIZATION METHODS AND SOFTWARE
, 1995
"... The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a pathgeneration procedure which is used to construct a piecewiselinear path from the current point to the Newton point; a step length acceptan ..."
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Cited by 213 (40 self)
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The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a pathgeneration procedure which is used to construct a piecewiselinear path from the current point to the Newton point; a step length
Sum Capacity of a Gaussian Vector Broadcast Channel
 IEEE Trans. Inform. Theory
, 2002
"... This paper characterizes the sum capacity of a class of nondegraded Gaussian vectB broadcast channels where a singletransmitter with multiple transmit terminals sends independent information to multiple receivers. Coordinat+[ is allowed among the transmit teminals, but not among the different recei ..."
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Cited by 279 (21 self)
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class of Gaussian channels whose saddlepoint satisfies a full rank condition. Furt her,t he sum capacity is achieved using a precoding method for Gaussian channels with additive side information noncausally known at the transmitter. The optimal precoding structure is shown t correspond to a decision
Stochastic Approximation Approach to Stochastic Programming
"... In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of th ..."
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Cited by 267 (20 self)
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class of convex stochastic problems. We extend the analysis to the case of convexconcave stochastic saddle point problems, and present (in our opinion highly encouraging) results of numerical experiments.
EFFICIENT SOLUTION OF LARGESCALE SADDLE POINT SYSTEMS ARISING IN RICCATIBASED BOUNDARY FEEDBACK STABILIZATION OF INCOMPRESSIBLE STOKES FLOW
, 2012
"... Abstract. We investigate numerical methods for solving largescale saddle point systems which arise during the feedback control of flow problems. We focus on the Stokes equations that describe instationary, incompressible flows for low and moderate Reynolds numbers. After a mixed finite element disc ..."
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conclude with numerical examples showcasing the performance of our preconditioned iterative saddle point solver.
A Class Of Iterative Methods For Solving Saddle Point Problems
 Numer. Math
, 1990
"... . We consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points. We are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations. We present an iterative method involving two ..."
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Cited by 75 (3 self)
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approximations of the Stokes equations. Key words. Saddle point problems, iterative solvers, mixed finite element methods. AMS subject classifications. 65F10, 65N20, 65N30. 1. Introduction. In this paper, we consider the solution of the system of linear equations A B t B 0 x y = f g (1
Results 1  10
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