Handbook of Semidefinite Programming pp 2965  Cite as
The Geometry of Semidefinite Programming
Chapter
Abstract
Consider the primaldual pair of optimization problems where
$$
\begin{gathered}
Min \left\langle {c,x} \right\rangle {\rm M}ax \left\langle {b,y} \right\rangle \hfill \\
(P) s.t. x \in K s.t. z \in K* (D) \hfill \\
Ax = b A*y + z = c \hfill \\
\end{gathered}
$$

X and Y are Euclidean spaces with dim X ≥ dim Y.

A : X → Y is a linear operator, assumed to be onto.

A^{*} : Y → X is its adjoint.

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

K^{*} := {z〈z,x〉≤ 0 ∀x∈K} 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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© Springer Science+Business Media New York 2000