A Convex Positivstellensatz

نویسنده

  • Jean B. Lasserre
چکیده

We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set K ⊂ Rn. Namely, we prove that almost all of them belong to a specific subset of the quadratic module generated by the concave polynomials that define K. In particular, almost all nonnegative convex polynomials are sums of squares. Mathematics Subject Classification (2000). Primary 14P10; Secondary 11E25 12D15 90C25.

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تاریخ انتشار 2008