Analysis of Bounds for Multilinear Functions

Authors:
Hong Seo Ryoo;Nikolaos V. Sahinidis
Affiliations:
University of Illinois at Chicago, Department of Mechanical Engineering, 842 W. Taylor Street, Chicago, Illinois 60607, USA (e-mail: hryoo@uic.edu);University of Illinois at Urbana-Champaign, Department of Chemical Engineering, 600 South Mathews Avenue, Urbana, Illinois 61801, USA (Corresponding author, e-mail: nikos@uiuc.edu ...
Venue:
Journal of Global Optimization
Year:
2001

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Abstract

We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave envelope for the product of p variables over Rp+.