Linear matrix inequality

In convex optimization, a linear matrix inequality (LMI) is an expression of the form

\operatorname{LMI}(y):=A_0+y_1A_1+y_2A_2+\cdots+y_m A_m\geq0\,

where

This linear matrix inequality specifies a convex constraint on y.

Applications

There are efficient numerical methods to determine whether an LMI is feasible (e.g., whether there exists a vector y such that LMI(y)  0), or to solve a convex optimization problem with LMI constraints. Many optimization problems in control theory, system identification and signal processing can be formulated using LMIs. Also LMIs find application in Polynomial Sum-Of-Squares. The prototypical primal and dual semidefinite program is a minimization of a real linear function respectively subject to the primal and dual convex cones governing this LMI.

Solving LMIs

A major breakthrough in convex optimization lies in the introduction of interior-point methods. These methods were developed in a series of papers and became of true interest in the context of LMI problems in the work of Yurii Nesterov and Arkadii Nemirovskii.

References

External links

This article is issued from Wikipedia - version of the Monday, March 21, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.