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• W1973836753 abstract "A truncated moment sequence (tms) in n variables and of degree d is a finite sequence y=(y α ) indexed by nonnegative integer vectors α:=(α 1,…,α n ) such that α 1+⋯+α n ≤d. Let K⊆ℝ n be a semialgebraic set. The truncated K-moment problem (TKMP) is: How can one check if a tms y admits a K-measure μ (a nonnegative Borel measure supported in K) such that $y_{alpha}= int_{K} x_{1}^{alpha_{1}}cdots x_{n}^{alpha_{n}},mathrm{d}mu$ for every α? This paper proposes a semidefinite programming (SDP) approach for solving TKMP. When K is compact, we get the following results: whether a tms admits a K-measure or not can be checked via solving a sequence of SDP problems; when y admits no K-measure, a certificate for the nonexistence can be found; when y admits one, a representing measure for y can be obtained from solving the SDP problems under some necessary and some sufficient conditions. Moreover, we also propose a practical SDP method for finding flat extensions, which in our numerical experiments always found a finitely atomic representing measure when it exists." @default.
• W1973836753 created "2016-06-24" @default.
• W1973836753 creator A5018024598 @default.
• W1973836753 creator A5080005590 @default.
• W1973836753 date "2012-09-28" @default.
• W1973836753 modified "2023-10-16" @default.
• W1973836753 title "A Semidefinite Approach for Truncated K-Moment Problems" @default.
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• W1973836753 doi "https://doi.org/10.1007/s10208-012-9132-x" @default.
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