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A cone programming approach to the bilinear matrix inequality problem and its geometry

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Abstract

We discuss an approach for solving the Bilinear Matrix Inequality (BMI) based on its connections with certain problems defined over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, we show that solving a given BMI is equivalent to examining the solution set of a suitably constructed Cone-LP or Cone-LCP. This approach facilitates our understanding of the geometry of the BMI and opens up new avenues for the development of the computational procedures for its solution.

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Authors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, 91109, Pasadena, CA, USA

    Mehran Mesbahi

  2. Department of Electrical Engineering - Systems, University of Southern California, 90089-2563, Los Angeles, CA, USA

    George P. Papavassilopoulos

Authors
  1. Mehran Mesbahi
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  2. George P. Papavassilopoulos
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Correspondence to Mehran Mesbahi.

Additional information

Research supported in part by the National Science Foundation under Grant CCR-9222734.

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Mesbahi, M., Papavassilopoulos, G.P. A cone programming approach to the bilinear matrix inequality problem and its geometry. Mathematical Programming 77, 247–272 (1997). https://doi.org/10.1007/BF02614437

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  • DOI: https://doi.org/10.1007/BF02614437

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