The 𝒮-cone and a primal-dual view on second-order representability
- The 𝒮-cone provides a common framework for cones of polynomials or exponen- tial 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 S-cone and its dual from the viewpoint of second-order representability. Extending results of Averkov and of Wang and Magron on the primal SONC cone, we provide explicit generalized second- order descriptions for rational S-cones and their duals.
Download full text files
Additional Services
| Author: | Helen NaumannGND, Thorsten TheobaldORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-722173 |
| DOI: | https://doi.org/10.1007/s13366-020-00512-9 |
| ISSN: | 2191-0383 |
| Parent Title (Multiple languages): | Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/10/12 |
| Date of first Publication: | 2020/10/12 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2023/03/21 |
| Tag: | Arithmetic-geometric exponentials; Dual cone; Positive polynomials; Second-order cone; Sums of non-negative circuit polynomials; 𝒮-cone |
| Volume: | 62 |
| Issue: | 1 |
| Page Number: | 21 |
| First Page: | 229 |
| Last Page: | 249 |
| Note: | MSC-Klassifikation: 90C23 - The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs |
| Note: | Open Access funding provided by Projekt DEAL. The work was partially supported through the project “Real Algebraic Geometry and Optimization” jointly funded by the German Academic Exchange Service DAAD and the Research Council of Norway RCN. |
| HeBIS-PPN: | 508545366 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Pxx Real algebraic and real analytic geometry / 14P10 Semialgebraic sets and related spaces |
| 52-XX CONVEX AND DISCRETE GEOMETRY / 52Axx General convexity / 52A20 Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
