The Geometry of Semidefinite Programming

  • Gábor Pataki
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 27)

Abstract

Consider the primal-dual pair of optimization problems
$$ \begin{gathered} Min \left\langle {c,x} \right\rangle {\rm M}ax \left\langle {b,y} \right\rangle \hfill \\ (P) s.t. x \in K s.t. z \in K* (D) \hfill \\ Ax = b A*y + z = c \hfill \\ \end{gathered} $$
where
  • X and Y are Euclidean spaces with dim X ≥ dim Y.

  • A : XY is a linear operator, assumed to be onto.

  • A* : YX is its adjoint.

  • K is a closed, convex, facially exposed cone in X.

  • K* := {z|〈z,x〉≤ 0 ∀xK} is the dual of K, also a closed, convex, facially exposed cone.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Gábor Pataki

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