arXiv subjects

Robert Weismantel

Publications and source records attributed to Robert Weismantel.

56 records · Page 4Linked to original sources

arXiv2005

Integer Polynomial Optimization in Fixed Dimension

We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an integer polynomial over the lattice points of a convex polytope, we show an algorithm to compute lower and upper bounds for the optimal value. For polynomials that are non-negative over the polytope, these sequences of bounds lead to a fully polynomial-time approximation scheme for the optimization problem.

math.OC↗

arXiv2004

Integral Function Bases

Integral bases, a minimal set of solutions to $Ax\leq b, x\in\Z^n$ that generate any other solution to $Ax\leq b, x\in\Z^n$, as a nonnegative integer linear combination, are always finite and are at the core of the Integral Basis Method introduced by Haus, K{ö}ppe and Weismantel. In this paper we present one generalization of the notion of integral bases to the nonlinear situation with the intention of creating an integral basis method also for nonlinear integer programming.

math.OC↗