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Generalized Truncated Moment Problems with Unbounded Sets

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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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Funding

Lei Huang and Ya-Xiang Yuan are partially supported by the National Natural Science Foundation of China (No. 12288201).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Lei Huang & Ya-Xiang Yuan

  2. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Jiawang Nie

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Lei Huang

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  1. Lei Huang
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  2. Jiawang Nie
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  3. Ya-Xiang Yuan
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Correspondence to Lei Huang.

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Huang, L., Nie, J. & Yuan, YX. Generalized Truncated Moment Problems with Unbounded Sets. J Sci Comput 95, 15 (2023). https://doi.org/10.1007/s10915-023-02139-z

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