8 research outputs found
Error bounds for monomial convexification in polynomial optimization
Get PDFConvex 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 .Comment: 33 pages, 2 figures, to appear in journa
Polyhedral subdivisions and functional forms for the convex envelopes of bilinear, fractional and other bivariate functions over general polytopes
No full textPolyhedral subdivisions and functional forms for the convex envelopes of bilinear, fractional and other bivariate functions over general polytopes
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