Thumbnail Image
Item

Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube

de Klerk,E.
; 
Laurent,M.
Abstract
We consider the problem of minimizing a polynomial on the hypercube $[0,1]^n$ and derive new error bounds for the hierarchy of semidefinite programming approximations to this problem corresponding to the Positivstellensatz of Schmüdgen [Math. Ann., 289 (1991), pp. 203–206]. The main tool we employ is Bernstein approximations of polynomials, which also gives constructive proofs and degree bounds for positivity certificates on the hypercube.
Description
Date
2010
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Tilburg University Research Output Collection
Show all metadata
Files
Thumbnail Image
hypercube_approx_paper_ML5-1_SIAMstyle.pdf
Adobe PDF, 502.84 KB
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
de Klerk, E & Laurent, M 2010, 'Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube', SIAM Journal on Optimization, vol. 20, no. 6, pp. 3104-3120. < http://dx.doi.org/10.1137/100790835 >
URI
https://hdl.handle.net/20.500.14602/53675
Embedded videos