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

From statwiki

Line 1: | Line 1: | ||

− | Rank Minimization Problem (RMP) has application in a variety of areas such as control, system identification, statistics and signal processing. | + | 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> | <math> | ||

− | \begin{ | + | \begin{array}{ l l } |

− | \mbox{minimize} & \mbox{ | + | \mbox{minimize} & \Tr X \\ |

+ | \mbox{subject to } & X \in C | ||

+ | \end{array} | ||

+ | </math> | ||

− | + | ||

− | + | ||

+ | 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