Difference between revisions of "a Rank Minimization Heuristic with Application to Minimum Order System Approximation"

From statwiki
Jump to: navigation, search
Line 3: Line 3:
 
\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} & \tr X \\
+
\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.
For
+
#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] \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] \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:

  1. Describing a generalization of the trace heuristic for genaral non-square matrices.
  2. Showing that the new heuristic can be reduced to an SDP, and hence effictively solved.
  3. Applying the mothod on the minimum order system approximation.