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Hyperbolic polynomials have their origins in partial diierential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial(More)
We show that the universal barrier function of a convex cone introduced by Nesterov and Nemirovskii is the logarithm of the characteristic function of the cone. This interpretation demonstrates the invariance of the universal barrier under the automorphism group of the underlying cone. This provides a simple method for calculating the universal barrier for(More)
A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the uni-variate polynomial t → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We(More)
To determine the effect of octreotide, octreotide with zinc, levamisole, and misoprostol on the bacterial translocation that develops in rats with acute pancreatitis (AP). A total of 36 rats were divided into six groups, each consisting of six rats. Only laparotomy was performed on the first group. Acute pancreatitis was performed on the second group.(More)
We characterize the barrier parameter of the optimal self{concordant barriers for homogeneous cones. In particular, we prove that for homogeneous convex cones this parameter is the same as the rank of the corresponding Siegel domain. We also provide lower bounds on the barrier parameter in terms of the Carath eodory number of the cone. The bounds are tight(More)