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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.

Keywords

Extreme Point Tangent Space Semidefinite Program Cone Program Strict Complementarity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Gábor Pataki

There are no affiliations available

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