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

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Rank Minimization Problem (RMP) has application in a variety of areas such as control, system identification, statistics and signal processing. Excep in some special cases RMP is known to be computationaly hard. 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.
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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.  
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<math>
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\begin{array}{ l l }
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\mbox{minimize} & \mbox{Rank } X \\
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\mbox{subject to } & X \in C
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\end{array}
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</math>
 +
 
  
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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{align}
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\begin{array}{ l l }
\mbox{minimize} & \mbox{Rank $X$} \\
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\mbox{minimize} & \Tr X \\
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\mbox{subject to } & X \in C
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\end{array}
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</math>
  
\end{align}
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</math>
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For

Revision as of 19:10, 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] \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} & \Tr X \\ \mbox{subject to } & X \in C \end{array} [/math]


For