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Friday, February 12, 2010 |
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Positive Polynomials Over Equality Constrained Unbounded Sets |
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A simple yet powerful algebraic connection between the set of polynomials that are
non-negative on a given closed domain and the set of polynomials that are
non-negative on the intersection of the same domain and the zero set of a given
polynomial is presented. This connection has interesting theoretical as well as
algorithmic implications. It yields a succinct derivation of copositive
programming reformulations for a big class of programs, generalizing Burer's
copositive formulation for mixed non-convex quadratically constrained quadratic
programming problems. As corollary of our main theorem we also obtain
representation theorems for positive polynomials on closed sets. |