Representing elementary semi-algebraic sets by a few polynomial inequalities: A constructive approach
| dc.creator | Averkov, Gennadiy | |
| dc.date | 2008-04-14 | |
| dc.date.accessioned | 2026-07-07T09:32:13Z | |
| dc.date.available | 2026-07-07T09:32:13Z | |
| dc.description | Let P be an elementary closed semi-algebraic set in R^d, i.e., there exist real polynomials p_1,...,p_s such that P= \{x \in R^d : p_1(x) \ge 0, >..., p_s(x) \ge 0 \}; in this case p_1,...,p_s are said to represent P. Denote by $n$ the maximal number of the polynomials from \{p_1,...,p_s\} that vanish in a point of P. If P is non-empty and bounded, we show that it is possible to construct n+1 polynomials representing P. Furthermore, the number n+1 can be reduced to n in the case when the set of points of P in which n polynomials from \{p_1,...,p_s\} vanish is finite. Analogous statements are also obtained for elementary open semi-algebraic sets. | |
| dc.description | 14 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0804.2134 | |
| dc.identifier | http://arxiv.org/abs/0804.2134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158737 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Optimization and Control | |
| dc.subject | 14P10; 14Q99; 03C10; 90C26 | |
| dc.title | Representing elementary semi-algebraic sets by a few polynomial inequalities: A constructive approach | |
| dc.type | text |