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Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
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Cited by 1334 (4 self)
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SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity
Implications of rational inattention
 JOURNAL OF MONETARY ECONOMICS
, 2002
"... A constraint that actions can depend on observations only through a communication channel with finite Shannon capacity is shown to be able to play a role very similar to that of a signal extraction problem or an adjustment cost in standard control problems. The resulting theory looks enough like fa ..."
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Cited by 514 (10 self)
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A constraint that actions can depend on observations only through a communication channel with finite Shannon capacity is shown to be able to play a role very similar to that of a signal extraction problem or an adjustment cost in standard control problems. The resulting theory looks enough like familiar dynamic rational expectations theories to suggest that it might be useful and practical, while the implications for policy are different enough to be interesting.
Cholesky Factorization of Semidefinite Toeplitz Matrices
 Lin. Alg. Appl
, 1997
"... It can be shown directly from consideration of the Schur algorithm that any n \Theta n semidefinite rank r Toeplitz matrix, T , has a factorization T = C r C T r with C r = C 11 C 12 0 0 where C 11 is r \Theta r and upper triangular. This paper explores the reliability of computing such a de ..."
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Cited by 6 (1 self)
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It can be shown directly from consideration of the Schur algorithm that any n \Theta n semidefinite rank r Toeplitz matrix, T , has a factorization T = C r C T r with C r = C 11 C 12 0 0 where C 11 is r \Theta r and upper triangular. This paper explores the reliability of computing such a
On the NesterovTodd direction in semidefinite programming
 SIAM JOURNAL ON OPTIMIZATION
, 1996
"... Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how ..."
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Cited by 134 (25 self)
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Nesterov and Todd discuss several pathfollowing and potentialreduction interiorpoint methods for certain convex programming problems. In the special case of semidefinite programming, we discuss how to compute the corresponding directions efficiently, how to view them as Newton directions, and how
Semidefinite Optimization
"... I Theory and algorithms for semidefinite optimization 1 1 Background: Convex sets and positive semidefinite matrices 2 1.1 Some fundamental notions..................... 3 1.1.1 Euclidean space........................ 3 ..."
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Cited by 3 (0 self)
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I Theory and algorithms for semidefinite optimization 1 1 Background: Convex sets and positive semidefinite matrices 2 1.1 Some fundamental notions..................... 3 1.1.1 Euclidean space........................ 3
Iterative Waterfilling for Gaussian Vector Multiple Access Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2001
"... This paper characterizes the capacity region of a Gaussian multiple access channel with vector inputs and a vector output with or without intersymbol interference. The problem of finding the optimal input distribution is shown to be a convex programming problem, and an efficient numerical algorithm ..."
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Cited by 309 (12 self)
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This paper characterizes the capacity region of a Gaussian multiple access channel with vector inputs and a vector output with or without intersymbol interference. The problem of finding the optimal input distribution is shown to be a convex programming problem, and an efficient numerical algorithm is developed to evaluate the optimal transmit spectrum under the maximum sum data rate criterion. The numerical algorithm has an iterative waterfilling int#j pret#4968 . It converges from any starting point and it reaches with in s per output dimension per transmission from the Kuser multiple access sum capacity af t#j just one it#4 at#49 . These results are also applicable to vector multiple access fading channels.
Regularization tools – a matlab package for analysis and solution of discrete illposed problems
 Numerical Algorithms
, 1994
"... The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents ..."
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Cited by 276 (8 self)
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The software described in this report was originally published in Numerical Algorithms 6 (1994), pp. 1–35. The current version is published in Numer. Algo. 46 (2007), pp. 189–194, and it is available from www.netlib.org/numeralgo and www.mathworks.com/matlabcentral/fileexchangeContents
The Quadratic Eigenvalue Problem
, 2001
"... . We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and t ..."
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Cited by 262 (21 self)
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. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software. Key words. quadratic eigenvalue problem, eigenvalue, eigenvector, matrix, matrix polynomial, secondorder differential equation, vibration, Millennium footbridge, overdamped system, gyroscopic system, linearization, backward error, pseudospectrum, condition number, Krylov methods, Arnoldi method, Lanczos method, JacobiDavidson method AMS subject classifications. 65F30 Contents 1 Introduction 2 2 Applications of QEPs 4 2.1 Secondorder differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Vibration analysis of structural systems ...
NevanlinnaPick interpolation for noncommutative analytic Toeplitz algebras
 OPERATOR THY
, 1998
"... The noncommutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to ..."
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Cited by 74 (16 self)
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The noncommutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic
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