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Journal Articles Journal of Complexity Year : 2014

Intrinsic complexity estimates in polynomial optimization

Bernd Bank
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Joos Heintz
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  • PersonId : 940434
Mohab Safey El Din


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.
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Dates and versions

hal-00815123 , version 1 (18-04-2013)
hal-00815123 , version 2 (10-02-2014)



Bernd Bank, Marc Giusti, Joos Heintz, Mohab Safey El Din. Intrinsic complexity estimates in polynomial optimization. Journal of Complexity, 2014, 30 (4), pp.430-443. ⟨10.1016/j.jco.2014.02.005⟩. ⟨hal-00815123v2⟩
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