Abstract
We briefly review the duality between moment problems and sums of squares (s.o.s.) representations of positive polynomials, and compare s.o.s. versus nonnegative polynomials. We then describe how to use such results to define convergent semidefinite programming relaxations in polynomial optimization as well as for the two related problems of computing the convex envelope of a rational function and finding all zeros of a system of polynomial equations.
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