A semidefinite approach for truncated \(K\)-moment problems (Q1928277)

From the authors' abstract: This paper proposes a semidefinite programming (SDP) approach for solving TKMP (that is, truncated \(K\)-moment problems). When \(K\) is compact, we get the following result: whether a tms (that is, a truncated moment sequence) admits a \(K\)-measure or not can be checked via solving a sequence of SDP problems; when \(y\) (that is, a finite sequence) 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.