Complexity of integer quasiconvex polynomial optimization

Abstract

The following case of integer polynomial optimization is considered: 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. An algorithm solving this problem is designed that belongs to the time-complexity class O(s) · lO(1) ·dO(n) ·2O(n3), where d ≥ 2 is an upper bound for the total degree of the polynomials involved and l denotes the maximum binary length of all coefficients. The algorithm is polynomial for a fixed number n of variables and represents a direct generalization of H.W.Lenstra’s algorithm [3] in integer linear optimization. Our complexity–result improves as well the one due to Bank et al. [1] as the one due to Khachiyan and Porkolab [2] for integer polynomial optimization in the considered case.

DOI: 10.1016/j.jco.2005.04.004

Cite this paper

@article{Heinz2005ComplexityOI, title={Complexity of integer quasiconvex polynomial optimization}, author={Sebastian Heinz}, journal={J. Complexity}, year={2005}, volume={21}, pages={543-556} }