Exact algorithms for linear matrix inequalities

  title={Exact algorithms for linear matrix inequalities},
  author={Didier Henrion and Simone Naldi and Mohab Safey El Din},
  journal={SIAM Journal on Optimization},
Let A(x) = A0 + x1A1 + · · · + xnAn be a linear matrix, or pencil, generated by given symmetric matrices A0, A1, . . . , An of size m with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex semialgebraic set called spectrahedron, described by a linear matrix inequality (LMI). We design an exact algorithm that, up to genericity assumptions on the input matrices, computes an exact algebraic representation of at least one point in the… CONTINUE READING
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