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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 ...