Analysis of Bounds for Multilinear Functions

Hong Seo Ryoo, Nikolaos V. Sahinidis

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)


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+.

Original languageEnglish
Pages (from-to)403-424
Number of pages22
JournalJournal of Global Optimization
Issue number4
Publication statusPublished - 2001 Apr
Externally publishedYes

Bibliographical 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.


  • Arithmetic intervals
  • Convex envelopes
  • Multiplicative programs

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics
  • Business, Management and Accounting (miscellaneous)
  • Computer Science Applications
  • Management Science and Operations Research


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