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The \(\mathcal{S}\)-cone and a primal-dual view on second-order representability. (English) Zbl 1471.90111

Summary: The \(\mathcal{S}\)-cone provides a common framework for cones of polynomials or exponential sums which establish non-negativity upon the arithmetic-geometric inequality, in particular for sums of non-negative circuit polynomials (SONC) or sums of arithmetic-geometric exponentials (SAGE). In this paper, we study the \(\mathcal{S}\)-cone and its dual from the viewpoint of second-order representability. Extending results of G. Averkov [SIAM J. Appl. Algebra Geom. 3, No. 1, 128–151 (2019; Zbl 1420.90043)] and of J. Wang and V. Magron [“A second order cone characterization for sums of nonnegative circuits”, Preprint, arXiv:1906.06179] on the primal SONC cone, we provide explicit generalized second-order descriptions for rational \(\mathcal{S}\)-cones and their duals.

MSC:

90C23 Polynomial optimization
14P10 Semialgebraic sets and related spaces
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
90C25 Convex programming
90C22 Semidefinite programming
11E10 Forms over real fields

Citations:

Zbl 1420.90043

Software:

REPOP
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Full Text: DOI arXiv

References:

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