Quadratic-programming criteria for copositive matrices
نویسندگان
چکیده
منابع مشابه
Copositive relaxation for general quadratic programming
We consider general, typically nonconvex, Quadratic Programming Problems. The Semi-deenite relaxation proposed by Shor provides bounds on the optimal solution, but it does not always provide suuciently strong bounds if linear constraints are also involved. To get rid of the linear side-constraints, another, stronger convex relaxation is derived. This relaxation uses copositive matrices. Special...
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Copositive optimization problems are particular conic programs: extremize linear forms over the copositive cone subject to linear constraints. Every quadratic program with linear constraints can be formulated as a copositive program, even if some of the variables are binary. So this is an NP-hard problem class. While most methods try to approximate the copositive cone from within, we propose a ...
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A standard quadratic problem consists of nding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semideenite programming relaxation is strengthened by replacing the cone of positive semideenite matrices by the cone of completely positive matrices (the positive semideenite matrices which allow a factorization F F T where F is some non-negative matrix). The...
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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1989
ISSN: 0024-3795
DOI: 10.1016/0024-3795(89)90076-1