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Intrinsic complexity estimates in polynomial optimization
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.
Keywords :
Polynomial optimization
Intrinsic complexity
Cited literature [47 references]
https://hal.inria.fr/hal-00815123
Contributor : Mohab Safey El Din <>
Submitted on : Monday, February 10, 2014 - 5:39:28 PM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM
Long-term archiving on: : Sunday, May 11, 2014 - 7:35:10 AM
Contributor : Mohab Safey El Din <>
Submitted on : Monday, February 10, 2014 - 5:39:28 PM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM
Long-term archiving on: : Sunday, May 11, 2014 - 7:35:10 AM
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