a Rank Minimization Heuristic with Application to Minimum Order System Approximation: Difference between revisions
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\begin{array}{ l l } | \begin{array}{ l l } | ||
\mbox{minimize} & \mbox{Rank } X \\ | \mbox{minimize} & \mbox{Rank } X \\ | ||
\mbox{subject to } & X \in C | \mbox{subject to: } & X \in C | ||
\end{array} | \end{array} | ||
</math> | </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. | 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{array}{ l l } | \begin{array}{ l l } | ||
\mbox{minimize} & \ | \mbox{minimize} & \mbox{Tr } X \\ | ||
\mbox{subject to } & X \in C | \mbox{subject to: } & X \in C | ||
\end{array} | \end{array} | ||
</math> | </math> | ||
This paper focuses on the following problems: | |||
#Describing a generalization of the trace heuristic for genaral non-square matrices. | |||
#Showing that the new heuristic can be reduced to an SDP, and hence effictively solved. | |||
#Applying the mothod on the minimum order system approximation. | |||
Revision as of 20:21, 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} & \mbox{Tr } X \\ \mbox{subject to: } & X \in C \end{array} }[/math]
This paper focuses on the following problems:
- Describing a generalization of the trace heuristic for genaral non-square matrices.
- Showing that the new heuristic can be reduced to an SDP, and hence effictively solved.
- Applying the mothod on the minimum order system approximation.