Complexity of integer quasiconvex polynomial optimization

@article{Heinz2005ComplexityOI,
  title={Complexity of integer quasiconvex polynomial optimization},
  author={Sebastian Heinz},
  journal={J. Complexity},
  year={2005},
  volume={21},
  pages={543-556}
}
We study a particular case of integer polynomial optimization: Minimize a polynomial F̂ on the set of integer points described by an inequality system F1 ≤ 0, . . . , Fs ≤ 0, where F̂ , F1, . . . , Fs are quasiconvex polynomials in n variables with integer coefficients. We design an algorithm solving this problem that belongs to the time-complexity class O(s) · lO(1) · dO(n) · 2O(n 3), where d ≥ 2 is an upper bound for the total degree of the polynomials involved and l denotes the maximum… CONTINUE READING