Paper Info
Title
The projective method for solving linear matrix inequalities
Abstract
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.
Year
DOI
Venue
1997
10.1007/BF02614434
Math. Program.
Keywords
DocType
Volume
linear matrix inequalities,projective method,linear matrix inequality,interior point methods,semidefinite programming,interior point method,system theory,polynomial time,convex optimization,projection method
Journal
77
Issue
ISSN
Citations 
2
0025-5610
27
PageRank 
References 
Authors
5.70
5
2
Name
Order
Citations
PageRank
Pascal Gahinet122977.15
Arkadi Nemirovski21642186.22