Journal of Global Optimization

, Volume 10, Issue 4, pp 425–437 | Cite as

A Convex Envelope Formula for Multilinear Functions

  • Anatoliy D. Rikun


Convex envelopes of multilinear functions on a unit hypercube arepolyhedral. This well-known fact makes the convex envelopeapproximation very useful in the linearization of non-linear 0–1programming problems and in global bilinear optimization. This paperpresents necessary and sufficient conditions for a convex envelope to be apolyhedral function and illustrates how these conditions may be used inconstructing of convex envelopes. The main result of the paper is a simpleanalytical formula, which defines some faces of the convex envelope of amultilinear function. This formula proves to be a generalization of the wellknown convex envelope formula for multilinear monomial functions.

Nonlinear 0–1 optimization linearization convex envelope concave extension bilinear programming global optimization 


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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Anatoliy D. Rikun
    • 1
  1. 1.East Coast Product GroupHamdenU.S.A.

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