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