concave envelope
English
Noun
concave envelope (plural concave envelopes)
- (mathematics, optimisation theory, of a function on a set) For a given set and real-valued function f defined on the convex hull conv(S), the lowest-valued concave function that overestimates or equals f over S.
- 1988, Ferenc Forgó, Nonconvex Programming, page 33,
- 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.
- 2004, C. A. Meyer, C. A. Floudas, Trilinear Monomials with Positive or Negative Domains: Facets of the Convex and Concave Envelopes, Christodoulos A. Floudas, Panos M. Pardalos (editors), Frontiers in Global Optimization, Springer, page 327,
- 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.
- 2012, Joseph Geunes, Demand Flexibility in Supply Chain Planning, Springer (Kluwer Academic), page 20,
- The cost of this order plan is linear in price, and the associated line must form a segment of the piecewise linear concave envelope.
- 1988, Ferenc Forgó, Nonconvex Programming, page 33,
Synonyms
- (optimisation theory): upper concave envelope
Coordinate terms
- convex envelope