Abstract.
We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set \({\mathbf{K}} \subset {\mathbb{R}}^n\). Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define \({\mathbf{K}}\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was completed with the support of the (french) ANR grant NT05-3-41612.
Received: 15 December 2007
Rights and permissions
About this article
Cite this article
Lasserre, J.B. Representation of nonnegative convex polynomials. Arch. Math. 91, 126–130 (2008). https://doi.org/10.1007/s00013-008-2687-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-008-2687-8