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Communication Dans Un Congrès Année : 2023

Signed Tropicalizations of Convex Semialgebraic Sets

Mateusz Skomra

Résumé

We study the signed valuations of convex semialgebraic sets defined over non-Archimedean fields. This is motivated by the efforts to understand the structure of semialgebraic sets that arise in convex optimization, such as the spectrahedra and the hyperbolicity cones. We give a full characterization of regular sets that are obtained as signed tropicalizations of convex semialgebraic sets, and we prove that the signed tropicalizations of hyperbolicity cones have a more restrictive structure. To obtain our results, we combine two recent advances in the area of tropical geometry: the study of signed valuations of general semialgebraic sets and the separation theorems for signed tropical convexities.
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Dates et versions

hal-04273455 , version 1 (07-11-2023)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Mateusz Skomra. Signed Tropicalizations of Convex Semialgebraic Sets. Extended Abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, Sep 2022, Bayreuth, Germany. pp.697-700, ⟨10.15495/EPub_UBT_00006809⟩. ⟨hal-04273455⟩
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