Consistency of moment systems. (English) Zbl 0840.90106

Summary: An important question in the study of moment problems is to determine when a fixed point in \(\mathbb{R}^n\) lies in the moment cone of vectors \((\int a_i d\mu)^n_1\), with \(\mu\) a nonnegative measure. In associated optimization problems it is also important to be able to distinguish between the interior and boundary of the moment case. Recent work of Dachuna-Castelle, Gamboa and Gassiat derived elegant computational characterizations for these problems, and for related questions with an upper bound on \(\mu\). Their technique involves a probabilistic interpretation and large deviations theory. In this paper a purely convex analytic approach is used, giving a more direct understanding of the underlying duality, and allowing the relaxation of their assumptions.


90C25 Convex programming
49J52 Nonsmooth analysis
65K05 Numerical mathematical programming methods
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