Jean B. Lasserre
Abstract:
We consider the generalized problem of moments (GPM) from a computational point of view and review various examples of applications in global optimization, probability, financial economics and optimal control, which all can be viewed as particular instances of the GPM. When the data of the GPM consist of polynomials and basic semi-algebraic sets, we provide a hierarchy of semidefinite programming (SDP) relaxations whose sequence of optimal values converges to the optimal value of the GPM. We also show how to handle sparsity in the data and define specific convergent relaxations for some large size problems.