Meaning of concave envelope | Babel Free

Definitions

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.

Examples

“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.”

CEFR level