Extreme copositive quadratic forms
نویسندگان
چکیده
منابع مشابه
Applications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملCopositive 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...
متن کاملQuadratic factorization heuristics for copositive programming
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 ...
متن کاملCopositive and semidefinite relaxations of the quadratic assignment problem
Semidefinite relaxations of the quadratic assignment problem (QAP ) have recently turned out to provide good approximations to the optimal value of QAP . We take a systematic look at various conic relaxations of QAP . We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it is hard to optimize over this cone, we also look ...
متن کاملOn Copositive Programming and Standard Quadratic Optimization Problems
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1966
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1966.19.197