# a Rank Minimization Heuristic with Application to Minimum Order System Approximation

$\begin{array}{ l l } \mbox{minimize} & \mbox{Rank } X \\ \mbox{subject to: } & X \in C \end{array}$
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. $\begin{array}{ l l } \mbox{minimize} & \mbox{Tr } X \\ \mbox{subject to: } & X \in C \end{array}$