Sufficient Conditions for a Real Polynomial to be a Sum of Squares
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.
Entry Submitted: 02/14/2007
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