A Survey of Semidefinite Programming Approaches to the Generalized Problem of Moments and Their Error Analysis [chapter]

Etienne de Klerk, Monique Laurent
2019 Association for Women in Mathematics Series  
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational functions, option pricing in finance, constructing quadrature schemes for numerical integration, and distributionally robust optimization. A usual solution approach, due to J.B. Lasserre, is to approximate the convex cone of positive Borel measures by finite
more » ... imensional outer and inner conic approximations. We will review some results on these approximations, with a special focus on the convergence rate of the hierarchies of upper and lower bounds for the general problem of moments that are obtained from these inner and outer approximations.
doi:10.1007/978-3-030-21170-7_1 fatcat:23ussbhb55az7gk5avubr5lbce