## 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.

### MSC:

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