固定维的多项式Optimization
Integer Polynomial Optimization in Fixed Dimension
摘要：
我们根据其计算复杂性，分类整数最优化问题的约束条件和目标函数是整系数多项式和变量的数量是固定的。对于在凸多胞体的格点上的整数多项式的优化问题，我们给出了一个计算最优值的上界的算法。对于多面体上的非负多项式，这些边界序列导致最优化问题的完全多项式时间近似方案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
