Representing simple d-dimensional polytopes by d polynomials
نویسندگان
چکیده
منابع مشابه
Representing simple d-dimensional polytopes by d polynomials
A polynomial representation of a convex d-polytope P is a finite set {p1(x), . . . , pn(x)} of polynomials over R such that P = ̆ x ∈ R : p1(x) ≥ 0 for every 1 ≤ i ≤ n ̄ . By s(d, P ) we denote the least possible number of polynomials in a polynomial representation of P. It is known that d ≤ s(d, P ) ≤ 2d − 1. Moreover, it is conjectured that s(d, P ) = d for all convex d-polytopes P. We confirm ...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2009
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-009-0280-y