Detecting global optimality and extracting solutions in GloptiPoly

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Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals (2007, methodology): “For more details about extracting minimizers from SOS relaxations or moment matrix methods, we refer to [9].”
A generalized flat extension theorem for moment matrices (2009, background): “Moreover the flat extension theorem of Curto and Fialkow permits to detect optimality of the relaxations and to extract global optimizers to the original optimization problem (see [9]).”
Revisiting two theorems of Curto and Fialkow on moment matrices (2005, methodology): “Henrion and Lasserre [16] propose the following procedure for computing v1, . . . , vr, whose details fit nicely within our algebraic setting.”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “Starting quite recently, a large number of papers appeared that propose the use of semidefinite relaxations, or convex conic relaxations, to solve polynomial constraint satisfaction and global optimization problems: see, e.g., Chesi and Garulli (2001), Jibetean and De Klerk (2003), Fujie and Kojima ”