Sufficient Conditions for a Real Polynomial to be a Sum of Squares

J.B. Lasserre(lasserrelaas.fr)

Abstract: We provide explicit sufficient conditions for a polynomial $f$ to be a sum of squares (s.o.s.), linear in the coefficients of $f$. All conditions are simple and provide an explicit description of a convex polyhedral subcone of the cone of s.o.s. polynomials of degree at most $2d$. We also provide a simple condition to ensure that $f$ is s.o.s., possibly after adding a constant.

Keywords: Real algebraic geomery; positive polynomials; sums of squares

Category 1: Global Optimization (Theory )

Category 2: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 3: Other Topics (Other )

Citation: Report #06789, LAAS, Toulouse, France. To appear in Archiv der Mathematik.

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Entry Submitted: 02/14/2007
Entry Accepted: 02/16/2007
Entry Last Modified: 02/14/2007

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