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Polynomial inequalities representing polyhedra
 Math. Program
"... Abstract. Our main result is that every ndimensional polytope can be described by at most (2n − 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an ndimensional pointed polyhedral cone we prove the bound 2n − 2 and for arbitrary polyhedra we get a cons ..."
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Cited by 8 (2 self)
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Abstract. Our main result is that every ndimensional polytope can be described by at most (2n − 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an ndimensional pointed polyhedral cone we prove the bound 2n − 2 and for arbitrary polyhedra we get a
The representation of polyhedra by polynomial inequalities
 Discrete Comput. Geom
"... Abstract. A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semialgebraic sets implies, as a very special case, that every ddimensional polyhedron admits a representation as the set of solutions of at most d(d+1)/2 polynomial inequalities. Even in this polyhedral ..."
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Cited by 9 (2 self)
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Abstract. A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semialgebraic sets implies, as a very special case, that every ddimensional polyhedron admits a representation as the set of solutions of at most d(d+1)/2 polynomial inequalities. Even in this polyhedral
Equality Cases for Two Polynomial Inequalities
"... We give a complete characterization of the equality cases for two recent polynomial inequalities. The proofs are based on simple interpolation and quadrature techniques. We discuss also the meaning and the sharpness of these inequalities. ..."
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We give a complete characterization of the equality cases for two recent polynomial inequalities. The proofs are based on simple interpolation and quadrature techniques. We discuss also the meaning and the sharpness of these inequalities.
POLYNOMIAL INEQUALITIES FOR NONCOMMUTING
"... Abstract. We prove an inequality for polynomials applied in a symmetric way to noncommuting operators. Key words. Ando inequality, Noncommuting, Symmetric functional calculus. AMS subject classifications. 15A60. 1. Introduction. J. von Neumann [9] proved an inequality about the norm of a polynomia ..."
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Abstract. We prove an inequality for polynomials applied in a symmetric way to noncommuting operators. Key words. Ando inequality, Noncommuting, Symmetric functional calculus. AMS subject classifications. 15A60. 1. Introduction. J. von Neumann [9] proved an inequality about the norm of a
Cyclic Homogeneous Polynomial Inequalities
, 2009
"... vol. 10, iss. 3, art. 67, 2009 Title Page Contents ..."
Global Optimization with Polynomials and the Problem of Moments
 SIAM Journal on Optimization
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
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Cited by 569 (47 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
Landau And Kolmogoroff Type Polynomial Inequalities
"... Let 0 < j < m n be integers. Denote by k k the norm kfk 2 = R 1 1 f 2 (x) exp( x 2 )dx: For various positive values of A and B we establish Kolmogoro type inequalities kf (j) k 2 Akf (m) k 2 +Bkfk 2 A k +B k ; with certain constants k e k ; which hold for every f 2 ..."
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2 n (n denotes the space of real algebraic polynomials of degree not exceeding n). For the particular case j = 1 and m = 2, we provide a complete characterisation of the positive constants A and B, for which the corresponding Landau type polynomial inequalities kf 0 k 2 Akf 00 k 2 +Bkfk
POLYNOMIAL INEQUALITIES FOR NONCOMMUTING OPERATORS ∗
"... Abstract. We proveaninequality forpolynomialsappliedinasymmetricway tononcommuting operators. Key words. Ando inequality, Noncommuting, Symmetric functional calculus. AMS subject classifications. 15A60. 1. Introduction. J. von Neumann [9] proved an inequality about the norm of a polynomial applied ..."
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Abstract. We proveaninequality forpolynomialsappliedinasymmetricway tononcommuting operators. Key words. Ando inequality, Noncommuting, Symmetric functional calculus. AMS subject classifications. 15A60. 1. Introduction. J. von Neumann [9] proved an inequality about the norm of a polynomial
Sum of Squares Programs and Polynomial Inequalities
"... Consider a given system of polynomial equations and inequalities, for instance: f1(x1, x2):= g1(x1, x2):= ..."
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Consider a given system of polynomial equations and inequalities, for instance: f1(x1, x2):= g1(x1, x2):=
Solving strict polynomial inequalities by Bernstein expansion
 In: Symbolic Methods in Control System Analysis and Design
, 1999
"... Introduction Many interesting control system design and analysis problems can be recast as systems of inequalities for multivariate polynomials in real variables. In particular, for linear timeinvariant systems, important control issues such as robust stability and robust performance can be reduce ..."
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Cited by 22 (1 self)
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Introduction Many interesting control system design and analysis problems can be recast as systems of inequalities for multivariate polynomials in real variables. In particular, for linear timeinvariant systems, important control issues such as robust stability and robust performance can
Results 1  10
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