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- Title
Error bounds for monomial convexification in polynomial optimization.
- Authors
Adams, Warren; Gupte, Akshay; Xu, Yibo
- 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.
- Subjects
POLYNOMIALS; CONVEX functions; MATHEMATICAL optimization; APPROXIMATION theory; MATHEMATICAL analysis
- Publication
Mathematical Programming, 2019, Vol 175, Issue 1/2, p355
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-018-1246-8