Supporting hyperplane

A convex set (in pink), a supporting hyperplane of (the dashed line), and the supporting half-space delimited by the hyperplane which contains (in light blue).

In geometry, a supporting hyperplane of a set in Euclidean space is a hyperplane that has both of the following two properties:[1]

  • is entirely contained in one of the two closed half-spaces bounded by the hyperplane,
  • has at least one boundary-point on the hyperplane.

Here, a closed half-space is the half-space that includes the points within the hyperplane.

  1. ^ Luenberger, David G. (1969). Optimization by Vector Space Methods. New York: John Wiley & Sons. p. 133. ISBN 978-0-471-18117-0.