*Researchers*: Anders Lindquist, Anders Blomqvist and Vanna Fanizza in
cooperation with C. I. Byrnes (Washington University, St Louis).

*Sponsors*: The Swedish Research Council (VR) and the Göran Gustafsson Foundation.

In a series of previous papers we derived a universal solution to
the generalized moment problem, with a nonclassical complexity
constraint, obtained by minimizing a strictly convex nonlinear
functional. This generalizes some the results in the project * Rational Nevanlinna-Pick interpolation with degree constraints* to
the more general setting of generalized moment problems. Moreover,
some connections to probability and statistics are being pursued. In another direction, these results are being applied to systems
identification using orthogonal basis function expansions. This solves
the long-standing problem of how to incorporate positivity constraints
in identification with orthonormal basis functions [C3][T1].

In [A3] we present a synthesis of our differentiable approach to the generalized moment problem. While our previously announced results required some differentiability hypotheses, this paper uses a weak form involving integrability and measurability hypotheses that are more in the spirit of the classical treatment of the generalized moment problem. Because of this generality, we can extend the existence and well-posedness of solutions to this problem to nonnegative, rather than positive, initial data in the complexity constraint. This has nontrivial implications in the engineering applications of this theory.