Consistency of moment systems. (English) Zbl 0840.90106

Lewis, A. S.

Can. J. Math. 47, No. 5, 995-1006 (1995).

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

Keywords:

convex analysis; maximum entropy; partially finite program; constraint qualification; moment problems; duality