Polynomial inequalities representing polyhedra
نویسندگان
چکیده
منابع مشابه
Polynomial inequalities representing polyhedra
Our main result is that every ro-dimensional polytope can be described by at most (2n — 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n — 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities. 1. I N T R O D U C T I O N By a striking result of...
متن کاملThe Representation of Polyhedra by Polynomial Inequalities
A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every ^-dimensional polyhedron admits a representation as the set of solutions of at most d(d + l) /2 polynomial inequalities. Even in this polyhedral case, however, no constructive proof is known, even if the quadratic upper bound is replaced by any boun...
متن کاملThree-Dimensional Polyhedra Can Be Described by Three Polynomial Inequalities
Bosse et al. conjectured that for every natural number d ≥ 2 and every ddimensional polytope P in Rd there exist d polynomials p0(x), . . . , pd−1(x) satisfying P = { x ∈ Rd : p0(x) ≥ 0, . . . , pd−1(x) ≥ 0} . We show that for dimensions d ≤ 3 even every d-dimensional polyhedron can be described by d polynomial inequalities. The proof of our result is constructive. 2000 Mathematics Subject Clas...
متن کاملOn Bernstein Type Inequalities for Complex Polynomial
In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.
متن کاملApproximating polyhedra with sparse inequalities
In this paper, we study how well one can approximate arbitrary polytopes using sparse inequalities. Our motivation comes from the use of sparse cutting-planes in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In ord...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2005
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-004-0563-2