Article ID: | iaor19981382 |
Country: | Netherlands |
Volume: | 77 |
Issue: | 2 |
Start Page Number: | 163 |
End Page Number: | 190 |
Publication Date: | May 1997 |
Journal: | Mathematical Programming |
Authors: | Gahinet Pascal, Nemirovski Arkadi |
Keywords: | semidefinite programming, interior point methods |
Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.