# Intrinsic complexity estimates in polynomial optimization

4 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
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.
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Journal articles

Cited literature [47 references]

https://hal.inria.fr/hal-00815123
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Submitted on : Monday, February 10, 2014 - 5:39:28 PM
Last modification on : Friday, January 21, 2022 - 3:21:47 AM
Long-term archiving on: : Sunday, May 11, 2014 - 7:35:10 AM

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### Citation

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

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