Algebraic Boundaries of Convex Semi-algebraic Sets
Algebraic Geometry
2014-11-04 v2 Optimization and Control
Abstract
We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalize the correspondence of facets of a polytope to the vertices of the dual polytope to general semi-algebraic convex bodies. In the general setup, exceptional families of extreme points might exist and we characterize them semi-algebraically. We also give an algorithm to compute a complete list of exceptional families, given the algebraic boundary of the dual convex set.
Cite
@article{arxiv.1405.7822,
title = {Algebraic Boundaries of Convex Semi-algebraic Sets},
author = {Rainer Sinn},
journal= {arXiv preprint arXiv:1405.7822},
year = {2014}
}
Comments
13 pages, 2 figures; Comments welcome