convex envelope

Definitions

1. 1

   Convex hull.

   • The polytopes are, by definition, the convex envelopes of finite sets of points of an affine space.
2. 2

   For a given set S⊆ℝⁿ and real-valued function f defined on the convex hull conv(S), the…

   For a given set S⊆ℝⁿ and real-valued function f defined on the convex hull conv(S), the highest-valued convex function that underestimates or equals f over S.

   • The concept of convex envelopes of nonconvex functions is a basic tool in theory and algorithms of global optimization, see e.g., Falk and Hoffman (1976), Horst and Tuy (1996), Horst et al. (2000).

The neighborhood

• synonymlower convex envelopeoptimisation theory