تقرير
Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming
| العنوان: | Maximizing Slice-Volumes of Semialgebraic Sets using Sum-of-Squares Programming |
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| المؤلفون: | Miller, Jared, Meroni, Chiara, Tacchi, Matteo, Velasco, Mauricio |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Algebraic Geometry |
| الوصف: | This paper presents an algorithm to maximize the volume of an affine slice through a given semialgebraic set. This slice-volume task is formulated as an infinite-dimensional linear program in continuous functions, inspired by prior work in volume computation of semialgebraic sets. A convergent sequence of upper-bounds to the maximal slice volume are computed using the moment-Sum-of-Squares hierarchy of semidefinite programs in increasing size. The computational complexity of this scheme can be reduced by utilizing topological structure (in dimensions 2, 3, 4, 8) and symmetry. This numerical convergence can be accelerated through the introduction of redundant Stokes-based constraints. Demonstrations of slice-volume calculation are performed on example sets. Comment: 28 pages, 5 figures, 10 tables |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.04438 |
| رقم الأكسشن: | edsarx.2403.04438 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |