A semidefinite programming approach to the generalized problem of moments

Authors:
Jean B. Lasserre
Affiliations:
LAAS-CNRS and Institute of Mathematics, LAAS, 7 Avenue du Colonel Roche, 31077, Toulouse cédex 4, France
Venue:
Mathematical Programming: Series A and B
Year:
2007

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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.