منابع مشابه
Preprint : Considering Copositivity Locally ∗
We say that a symmetric matrix A is copositive if vTAv ≥ 0 for all nonnegative vectors v. The main result of this paper is a characterization of the cone of feasible directions at a copositive matrix A, i.e., the convex cone of symmetric matrices B such that there exists δ > 0 satisfying A + δB being copositive. This cone is described by a set of linear inequalities on the elements of B constru...
متن کاملConsidering copositivity locally
Let A be an element of the copositive cone COP. A zero u of A is a nonnegative vector whose elements sum up to one and such that uTAu = 0. The support of u is the index set suppu ⊂ {1, . . . , n} corresponding to the nonzero entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support suppv is a strict subset of suppu. Our main result is a char...
متن کاملCopositivity and constrained fractional quadratic problems
We provide Completely Positive and Copositive Optimization formulations for the Constrained Fractional Quadratic Problem (CFQP) and Standard Fractional Quadratic Problem (StFQP). Based on these formulations, Semidefinite Programming (SDP) relaxations are derived for finding good lower bounds to these fractional programs, which can be used in a global optimization branch-and-bound approach. Appl...
متن کاملAn LP-based Algorithm to Test Copositivity
A symmetric matrix is called copositive if it generates a quadratic form taking no negative values over the nonnegative orthant, and the linear optimization problem over the set of copositive matrices is called the copositive programming problem. Recently, many studies have been done on the copositive programming problem (see, for example, [14, 5]). Among others, several branch and bound type a...
متن کاملTesting copositivity with the help of difference-of-convex optimization
We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We the...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00351-2