a Rank Minimization Heuristic with Application to Minimum Order System Approximation: Difference between revisions
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Rank Minimization Problem (RMP) has application in a variety of areas such as control, system identification, statistics and signal processing. | Rank Minimization Problem (RMP) has application in a variety of areas such as control, system identification, statistics and signal processing. Except in some special cases RMP is known to be computationaly hard. | ||
<math> | |||
\begin{array}{ l l } | |||
\mbox{minimize} & \mbox{Rank } X \\ | |||
\mbox{subject to } & X \in C | |||
\end{array} | |||
</math> | |||
If the matrix is symmetric and positive semidifinite, trace minimization is a very effective heuristic for rank minimization problem. The trace minimization results in a semidefinite problem which can be easily solved. | |||
<math> | <math> | ||
\begin{ | \begin{array}{ l l } | ||
\mbox{minimize} & \mbox{ | \mbox{minimize} & \Tr X \\ | ||
\mbox{subject to } & X \in C | |||
\end{array} | |||
</math> | |||
For |
Revision as of 20:10, 23 November 2010
Rank Minimization Problem (RMP) has application in a variety of areas such as control, system identification, statistics and signal processing. Except in some special cases RMP is known to be computationaly hard. [math]\displaystyle{ \begin{array}{ l l } \mbox{minimize} & \mbox{Rank } X \\ \mbox{subject to } & X \in C \end{array} }[/math]
If the matrix is symmetric and positive semidifinite, trace minimization is a very effective heuristic for rank minimization problem. The trace minimization results in a semidefinite problem which can be easily solved.
[math]\displaystyle{
\begin{array}{ l l }
\mbox{minimize} & \Tr X \\
\mbox{subject to } & X \in C
\end{array}
}[/math]
For