Integer Polynomial Optimization in Fixed Dimension

Details Integer Polynomial Optimization in Fixed Dimension Integer Polynomial Optimization in Fixed Dimension

2004-10-05

arxiv.org/abs/math/0410111v2

Mathematics

Optimization and Control

In this revised version we include a stronger complexity bound on our algorithm. Our algorithm is in fact an FPTAS (fully poly

Scientific paper

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.

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