Generalized truncated moment problems with unbounded sets

Lei Huang; Jiawang Nie; Ya-Xiang Yuan

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arXiv · 2208.00354

Generalized truncated moment problems with unbounded sets

Lei Huang·Jiawang Nie·Ya-Xiang Yuan

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Abstract

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.

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Lei Huang, Jiawang Nie, Ya-Xiang Yuan. 2022-07-31. Generalized truncated moment problems with unbounded sets. https://arxiv.org/abs/2208.00354

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