A Variational Approach to Copositive Matrices
نویسندگان
چکیده
منابع مشابه
A 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.
متن کاملConstructing 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 کاملA Copositive Programming Approach to Graph Partitioning
We consider 3-partitioning the vertices of a graph into sets S1, S2 and S3 of specified cardinalities, such that the total weight of all edges joining S1 and S2 is minimized. This problem is closely related to several NP-hard problems like determining the bandwidth or finding a vertex separator in a graph. We show that this problem can be formulated as a linear program over the cone of complete...
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...
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ژورنال
عنوان ژورنال: SIAM Review
سال: 2010
ISSN: 0036-1445,1095-7200
DOI: 10.1137/090750391