NONLINEAR VARIATIONAL PROBLEMS, MOMENTS AND MOMENT COMPLETIONS

The standard (nonlinear) problem of optimal control or variational calculus can be con-
verted into a (linear) problem over the space of measures. Functional analytic considera-
tions of the variational problem further reduces this problem to a problem of moments with
respect to specic classes of (orthogonal) polynomials. While SDP methods have been used
to solve the reformulation, analytically this problem is convertible to nding measures for
which some moments or linear combination of moments are specied and a functional of
other moments are minimized. In particular, this is a moment completion problem where
not only completions are sought, but a \best" completion is expected.
In this talk, we give a detailed presentation of this reformulation and give some recent
results on completion of moment problems. Optimal completions presents a large area of
open problems.
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