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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Descartes Rule of Signs and Linear Programming
verfasst von : Carla Fidalgo, Alexander Kovačec
Erschienen in: Mathematical Methods in Engineering
Verlag: Springer Netherlands
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Abstract
Let \(\Delta=\{(x,y):x+y=1, x,y \geq 0\}\) be the 1-simplex and for \(m\geq 2\) consider the (binary) formUsing linear programming and a little known refinement of Descartes’ rule of signs due to Laguerre, it is shown that if all \(u_i\geq 0\) and F is nonzero and nonnegative on \(\Delta,\) then it assumes there exactly one global minimum. The investigation is motivated by a question concerning sum of squares representation.
$$F(x,y)=u_n x^n +u_0 y^n -\sum_{\begin{array}{c} i, j\geq 1 \\ i+j=n\end{array}} u_i x^i y^j.$$