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. 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]