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A rank minimization heuristic with application to minimum order system approximation
Variable control system analysis and controller synthesis matrix rank linear matrix inequality (lmi) the positive semi-definite matrix variables
2015/8/11
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices
Positive semi-definite matrix convex sets functions half positive definite matrix distance data
2015/8/11
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize thi...
Rank minimization and applications in system theory
Matrix the convex set system identification statistics signal processing
2015/8/11
In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification...
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
2015/7/10
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
Log-Det Heuristic for Matrix Rank Minimization with Applications to Hankel and Euclidean Distance Matrices
Log-Det Heuristic Matrix Rank Minimization Applications Hankel Euclidean Distance Matrices
2015/7/10
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize thi...
Rank Minimization and Applications in System Theory
Rank Minimization Applications System Theory
2015/7/10
In this tutorial paper, we consider the problem of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification...
Non-Convex Rank Minimization via an Empirical Bayesian Approach
Non-Convex Rank Minimization via Empirical Bayesian Approach
2012/9/19
In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem.Consequently, the convex nuclear ...
Penalty Decomposition Methods for Rank Minimization
rank minimization penalty decomposition methods matrix completion
2010/10/21
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first show that a class of matrix optimization problems can be solved a...