Abstract : It is known that point searching in basic semialgebraic sets and the search for globally minimal points in polynomial optimization tasks can be carried out using $(s\,d)^{O(n)}$ arithmetic operations, where $n$ and $s$ are the numbers of variables and constraints and $d$ is the maximal degree of the polynomials involved.\spar \noindent We associate to each of these problems an intrinsic system degree which becomes in worst case of order $(n\,d)^{O(n)}$ and which measures the intrinsic complexity of the task under consideration.\spar \noindent We design non-uniformly deterministic or uniformly probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.
https://hal.inria.fr/hal-00815123
Contributeur : Mohab Safey El Din
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Soumis le : lundi 10 février 2014 - 17:39:28
Dernière modification le : mardi 17 avril 2018 - 11:33:47
Document(s) archivé(s) le : dimanche 11 mai 2014 - 07:35:10
