Intrinsic complexity estimates in polynomial optimization
Bernd Bank, Giusti, Marc, Joos Heintz, Mohab Safey El Din · arXiv (Cornell University) · 2013
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 oindent 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 oindent We design non-uniformly deterministic or uniformly probabilistic algorithms of intrinsic, quasi-polynomial complexity which solve these problems.