A Convex Envelope Formula for Multilinear Functions |
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Authors: | Anatoliy D Rikun |
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Institution: | (1) East Coast Product Group, 45 Winnett St., Hamden, CT, 06517, U.S.A. |
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Abstract: | 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. |
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Keywords: | Nonlinear 0– 1 optimization linearization convex envelope concave extension bilinear programming global optimization |
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