Abstract

A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interior-point methods. In this paper, we will consider two classes of optimization problems with LMI constraints: ffl The semidefinite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semidefinite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable technique for obtaining bounds on the solution of NP-hard problems.

Citations