A Survey of the S-Lemma

  title={A Survey of the S-Lemma},
  author={Imre P{\'o}lik and Tam{\'a}s Terlaky},
  journal={SIAM Rev.},
In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry, and linear algebra as well. These were all active research areas, but as there was little interaction between researchers in these different areas, their results remained mainly isolated. Here we give a unified analysis of the… 

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