In convex optimization, a linear matrix inequality (LMI) is an expression of the form where This linear matrix inequality specifies a convex constraint on
Many optimization problems in control theory, system identification and signal processing can be formulated using LMIs.
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.
A major breakthrough in convex optimization was 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.