concave envelope

Definitions

1. 1

   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 lowest-valued concave function that overestimates or equals f over S.

   • No immediate use of Theorem 4 can be made computationally since, with the exception of a few special cases (e.g. rectangular S and separable f) it is very hard to construct concave envelopes and convex hulls.
   • Explicit expressions defining the facets of the convex and concave envelopes for trilinear monomials, with positive or negative bounded domains for each variable, are derived in this paper.
   • The cost of this order plan is linear in price, and the associated line must form a segment of the piecewise linear concave envelope.

The neighborhood