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Moments, sums of squares, and tropicalization

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This research demonstrates how tropicalization aids in understanding duals of cones related to nonnegative polynomials and sums of squares.

Tropicalization provides insights into the duals of cones formed by nonnegative polynomials.
Explicit combinatorial descriptions are given for the moment and pseudomoment cones through tropicalization.
Examples highlight significant limitations in sums of squares approximations of nonnegative polynomials.
The moment and pseudomoment cones remain closed under Hadamard products when defined by binomial inequalities.

Blekherman et al. (2025) studied this question.

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This research demonstrates how tropicalization aids in understanding duals of cones related to nonnegative polynomials and sums of squares.