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The projective method for solving linear matrix inequalities

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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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Authors and Affiliations

  1. INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153, Le Chesnay Cedex, France

    Pascal Gahinet

  2. Faculty of Industrial Engineering and Management, Technion, 32000 Technion City, Haifa, Israel

    Arkadi Nemirovski

Authors
  1. Pascal Gahinet
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  2. Arkadi Nemirovski
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Correspondence to Arkadi Nemirovski.

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Gahinet, P., Nemirovski, A. The projective method for solving linear matrix inequalities. Mathematical Programming 77, 163–190 (1997). https://doi.org/10.1007/BF02614434

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  • DOI: https://doi.org/10.1007/BF02614434

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