论文标题
无限制集的通用截短的力矩问题
Generalized truncated moment problems with unbounded sets
论文作者
论文摘要
本文研究了无限制集合的广义截短的力矩问题。首先，我们研究截短矩锥的几何特性及其非负多项式的双锥。通过均质化技术，我们给出了瞬间弛豫的收敛层次结构，以近似这些锥体。有了它们，我们提供了一种瞬间的方法，用于解决无限制集的通用截短力矩问题。可以通过建议的方法获得有限的原子代表措施或证书的不存在证书。还提供了数值实验和应用。
This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a convergent hierarchy of Moment-SOS relaxations for approximating these cones. With them, we give a Moment-SOS method for solving generalized truncated moment problems with unbounded sets. Finitely atomic representing measures, or certificates for their nonexistence, can be obtained by the proposed method. Numerical experiments and applications are also given.
