منابع مشابه
Constructing copositive matrices from interior matrices
Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ Rn|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form xT Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not the sum of...
متن کاملEla Constructing Copositive Matrices from Interior Matrices
Abstract. Let A be an n by n symmetric matrix with real entries. Using the l1-norm for vectors and letting S 1 = {x ∈ R|||x||1 = 1, x ≥ 0}, the matrix A is said to be interior if the quadratic form x Ax achieves its minimum on S 1 in the interior. Necessary and sufficient conditions are provided for a matrix to be interior. A copositive matrix is referred to as being exceptional if it is not th...
متن کاملOn the maximal angle between copositive matrices
Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle θmax(Cn) between two copositive matrices of order n [J.-B. Hiriart-Urruty and A. Seeger. A variational approach to copositive matrices. SIAM Rev., 52:593–629, 2010.]. They have proved that θmax(C2) = 3 4 π and conjectured that θmax(Cn) is equal to 3 4 π for all n ≥ 2. In this note, their conjecture is disprov...
متن کاملAn algorithm for determining copositive matrices
In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of T̂ = {y ∈ ∆m|β y ≤ 0} on the standard simplex ∆m, where each component of the vector β is -1, 0 or 1.
متن کاملA Variational Approach to Copositive Matrices
This work surveys essential properties of the so-called copositive matrices, the study of which is spread over more than fifty-five years. Special emphasis is given to variational aspects related to the concept of copositivity. In addition, some new results on the geometry of the cone of copositive matrices are presented here for the first time.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.08.008