Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere

Abstract We consider the generalized moment problem (GMP) over simplex and sphere. This is a rich setting it contains NP-hard problems as special cases, like constructing optimal cubature schemes rational optimization. Using reformulation-linearization technique (RLT) Lasserre-type hierarchies, relaxations of are introduced analyzed. For our analysis we assume throughout existence dual solution well strong duality. GMP prove convergence rate O (1/ r ) for linear programming, RLT-type hierarchy, where level using quantitative version Pólya’s Positivstellensatz. As an extension recent result by Fang Fawzi (Math Program, 2020. https://doi.org/10.1007/s10107-020-01537-7 Lasserre hierarchy (Lasserre in Math Program 112(1):65–92, 2008. https://doi.org/10.1007/s10107-006-0085-1 sphere has $$O(1/r^2)$$ O ( 1 / r 2 ) . Moreover, show RLT-relaxation generalization minimizing forms degree d simplex, De Klerk et al. (J Theor Comput Sci 361(2–3):210–225, 2006).