Error bounds for monomial convexification in polynomial optimization

Warren Adams, Akshay Gupte, Yibo Xu

Research output: Contribution to journalArticlepeer-review

Abstract

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of . This implies additive error bounds for relaxing a polynomial optimization problem by convexifying each monomial separately. Our main error bounds depend primarily on the degree of the monomial, making them easy to compute. Since monomial convexification studies depend on the bounds on the associated variables, in the second part, we conduct an error analysis for a multilinear monomial over two different types of box constraints. As part of this analysis, we also derive the convex hull of a multilinear monomial over .
Original languageEnglish
Pages (from-to)355-393
Number of pages39
JournalMathematical programming
Volume175
Issue number1-2
DOIs
Publication statusPublished - 27 Mar 2018

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