Analysis of Bounds for Multilinear Functions

Hong Seo Ryoo; Nikolaos V. Sahinidis

doi:10.1023/A:1011295715398

Analysis of Bounds for Multilinear Functions

Hong Seo Ryoo, Nikolaos V. Sahinidis

Research output: Contribution to journal › Article › peer-review

41 Citations (Scopus)

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 ℝ^p₊.

Original language	English
Pages (from-to)	403-424
Number of pages	22
Journal	Journal of Global Optimization
Volume	19
Issue number	4
DOIs	https://doi.org/10.1023/A:1011295715398
Publication status	Published - 2001 Apr
Externally published	Yes

Keywords

Arithmetic intervals
Convex envelopes
Multiplicative programs

ASJC Scopus subject areas

Computer Science Applications
Management Science and Operations Research
Control and Optimization
Applied Mathematics

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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+.",

keywords = "Arithmetic intervals, Convex envelopes, Multiplicative programs",

author = "Ryoo, {Hong Seo} and Sahinidis, {Nikolaos V.}",

note = "Funding Information: We are grateful for partial financial support from the DuPont Educational Aid Program, the Mobil Technology Company, the University of Illinois Research Board, and the National Science Foundation under grant DMII 94-141615 and CAREER Award 95-02722 to N.V.S.",

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AU - Sahinidis, Nikolaos V.

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PY - 2001/4

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N2 - 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+.

AB - 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+.

KW - Arithmetic intervals

KW - Convex envelopes

KW - Multiplicative programs

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Analysis of Bounds for Multilinear Functions

Abstract

Keywords

ASJC Scopus subject areas

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