论文标题
关于用弗里茨约翰条件加强多项式优化的精确性
On the exactness for polynomial optimization strengthened with Fritz John conditions
论文作者
论文摘要
我们利用与[Arxiv：2205.04254（2022）]中相同的技术，在更一般的条件下，在多项式不等式定义的基本半代数集中提供了多项式非阴性的某些表示。基于每个表示形式，我们获得了半限定程序，该程序返回一系列值，该值有限收敛到通用假设下给定多项式优化问题的最佳值。因此，我们可以准确地计算出由基本凸半代数集的任何多项式的最小值，该凸由凹的多项式不等式定义。
We utilize the same technique as in [arXiv:2205.04254 (2022)] to provide some representations of polynomials non-negative on a basic semi-algebraic set, defined by polynomial inequalities, under more general conditions. Based on each representation, we obtain semidefinite programs which return a sequence of values that finitely converges to the optimal value of a given polynomial optimization problem under generic assumption. Consequently, we can compute exactly the minimal value of any polynomial over a basic convex semi-algebraic set which is defined by the inequalities of concave polynomials.
