The Projective Method for solving linear matrix inequalities

The Projective Method for solving linear matrix inequalities

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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: ,
Keywords: semidefinite programming, interior point methods
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.

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