Abstract
We consider the generalized problem of moments (GPM) from a computational point of view and provide a hierarchy of semidefinite programming relaxations whose sequence of optimal values converges to the optimal value of the GPM. We then investigate in detail various examples of applications in optimization, probability, financial economics and optimal control, which all can be viewed as particular instances of the GPM.
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This work was supported by french ANR-grant NT05-3-41612, and part of it was completed in January 2006 while the author was a member of IMS, the Institute for Mathematical Sciences of NUS (The National University of Singapore).
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Lasserre, J.B. A semidefinite programming approach to the generalized problem of moments. Math. Program. 112, 65–92 (2008). https://doi.org/10.1007/s10107-006-0085-1
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DOI: https://doi.org/10.1007/s10107-006-0085-1