a Rank Minimization Heuristic with Application to Minimum Order System Approximation
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