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

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\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} & \ | + | \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. | |

− | + | #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:

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