[Polynômes positifs sur des produits fibrés]
Nous présentons une interprétation algébrique (dans le langage des produits fibrés de variétés algébriques) de résultats récents en théorie de l'optimisation concernant la structure de polynômes positifs (sur un sous ensemble compact et semi-algébrique ) qui satisfont certaines conditions de séparation des variables dans leurs monômes. Ceci offre la perspective d'un traitement uniforme de tels polynômes, positifs sur K non-compact, ou non-semi-algébrique, ainsi que pour des polynômes en un nombre dénombrable de variables.
Recent investigations in optimization theory concerning the structure of positive polynomials with a sparsity pattern are interpreted in the more invariant language of (iterated) fibre products of real algebraic varieties. This opens the perspective of treating on a unifying basis the cases of positivity on unbounded supports, on non-semialgebraic supports, or of polynomials depending on countably many variables.
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@article{CRMATH_2007__344_11_681_0,
author = {Kuhlmann, Salma and Putinar, Mihai},
title = {Positive polynomials on fibre products},
journal = {Comptes Rendus. Math\'ematique},
pages = {681--684},
publisher = {Elsevier},
volume = {344},
number = {11},
year = {2007},
doi = {10.1016/j.crma.2007.04.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.04.009/}
}
TY - JOUR AU - Kuhlmann, Salma AU - Putinar, Mihai TI - Positive polynomials on fibre products JO - Comptes Rendus. Mathématique PY - 2007 SP - 681 EP - 684 VL - 344 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.04.009/ DO - 10.1016/j.crma.2007.04.009 LA - en ID - CRMATH_2007__344_11_681_0 ER -
%0 Journal Article %A Kuhlmann, Salma %A Putinar, Mihai %T Positive polynomials on fibre products %J Comptes Rendus. Mathématique %D 2007 %P 681-684 %V 344 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.04.009/ %R 10.1016/j.crma.2007.04.009 %G en %F CRMATH_2007__344_11_681_0
Kuhlmann, Salma; Putinar, Mihai. Positive polynomials on fibre products. Comptes Rendus. Mathématique, Tome 344 (2007) no. 11, pp. 681-684. doi : 10.1016/j.crma.2007.04.009. http://www.numdam.org/articles/10.1016/j.crma.2007.04.009/
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⁎ Partially supported by an NSERC Discovery Grant, Canada and the National Science Foundation-USA.
