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On Low Complexity Robust Beamforming With Positive Semidefinite Constraints
"... Abstract—This paper addresses the problem of robust beamforming for generalrank signal models with norm bounded uncertainties in the desired and received signal covariance matrices as well as positive semidefinite constraints on the covariance matrices. Two novel minimum variance robust beamformers ..."
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Cited by 3 (0 self)
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Abstract—This paper addresses the problem of robust beamforming for generalrank signal models with norm bounded uncertainties in the desired and received signal covariance matrices as well as positive semidefinite constraints on the covariance matrices. Two novel minimum variance robust
WHEN DOES THE POSITIVE SEMIDEFINITENESS CONSTRAINT HELP IN LIFTING PROCEDURES?
, 2001
"... We study the liftandproject procedures of Lovász and Schrijver for 01 integer programming problems. We prove that the procedure using the positive semidefiniteness constraint is not better than the one without it, in the worst case. Various examples are considered. We also provide geometric condi ..."
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Cited by 29 (2 self)
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We study the liftandproject procedures of Lovász and Schrijver for 01 integer programming problems. We prove that the procedure using the positive semidefiniteness constraint is not better than the one without it, in the worst case. Various examples are considered. We also provide geometric
Second Order Cone Programming Relaxation of Positive Semidefinite Constraints
, 2001
"... The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of ex ..."
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Cited by 10 (0 self)
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The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways
Approximating Quadratic Programs with Positive Semidefinite Constraints
"... We describe a polynomial time approximation algorithm to the problem of maximizing a quadratic form subject to quadratic constraints specified by PSD matrices. A special case, that has applications for clustering [CW04], is optimizing quadratic forms over the unit cube. Approximation algorithms with ..."
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Cited by 1 (0 self)
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with similar guarantees are known [Nes98, NRT99, Meg01, CW04], and there is evidence that this factor is optimal [ABH +]. The following analysis is particularly simple. Consider the following quadratic program: max x T Ax i = 1,..., m x T Aix ≤ 1 (1) where, x ∈ R n, and A1, A2,..., Am are positive semidefinite
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 780 (22 self)
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is contained in the socalled kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input spaceclassical model selection
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 557 (12 self)
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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
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1231 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 872 (14 self)
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and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important
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
Results 1  10
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1,506,859