Under relative interior assumptions, the infinite-dimensional dual of the GMP attains its optimum and each SOS relaxation is attained for supports that are compact basic semialgebraic sets with nonempty interior or real radical varieties defined by Gröbner bases.
Convergence of L asserre’s hierarchy: the general case
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Duality attainment and strict feasibility of the generalized moment problem and its relaxations
Under relative interior assumptions, the infinite-dimensional dual of the GMP attains its optimum and each SOS relaxation is attained for supports that are compact basic semialgebraic sets with nonempty interior or real radical varieties defined by Gröbner bases.