document: Minimizing blossoms under symmetric linear constraints In this paper , we show that there exists a close dependence between the control polygon of a polynomial and the minimum of its blossom under symmetric linear constraints . We consider a given minimization problem P , for which a unique solution will be a point delta on the Bezier curve . For the minimization function f , two sufficient conditions exist that ensure the uniqueness of the solution , namely , the concavity of the control polygon of the polynomial and the characteristics of the Polya frequency-control polygon where the minimum coincides with a critical point of the polynomial . The use of the blossoming theory provides us with a useful geometrical interpretation of the minimization problem . In addition , this minimization approach leads us to a new method of discovering inequalities about the elementary symmetric polynomials
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