The Projective Method for solving linear matrix inequalities

Data:	1997
Resum:	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. .
Drets:	Tots els drets reservats
Llengua:	Anglès
Document:	article ; recerca ; Versió publicada
Matèria:	Linear matrix inequalities ; Semidefinite programming ; Interior point methods
Publicat a:	Mathematical Programming, vol. 77 n. 2 (1997) p. 163-190, ISSN 0025-5610

28 p, 1.1 MB

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