A refined error analysis for fixed-degree polynomial optimization over the simplex
Sun,Zhao
Sun,Zhao
Abstract
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex. This problem is well known to be NP-hard, since it contains the maximum stable set problem in combinatorial optimization as a special case. In this paper, we revisit a known upper bound obtained by taking the minimum value on a regular grid, and a known lower bound based on P\'olya's representation theorem. More precisely, we consider the difference between these two bounds and we provide upper bounds for this difference in terms of the range of function values. Our results refine the known upper bounds in the quadratic and cubic cases, and they asymptotically refine the known upper bound in the general case.
Description
15 pages
Date
2014-09-11
Journal Title
Journal ISSN
Volume Title
Publisher
Research Projects
Organizational Units
Journal Issue
Keywords
polynomial optimization over the simplex, global optimization, nonlinear optimization, 90C30, 90C60
Citation
Sun, Z 2014, 'A refined error analysis for fixed-degree polynomial optimization over the simplex', Journal of the Operations Research Society of China, vol. 2, no. 3, pp. 379-393. https://doi.org/10.1007/s40305-014-0057-8
License
info:eu-repo/semantics/restrictedAccess