Hyperbolic Polynomials and Convex Analysis

Hyperbolic Polynomials and Convex Analysis

A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate 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 present a powerful new such construction, an...

Hyperbolic Polynomials and Interior Point Methods for Convex Programming

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 inequalities. The function F (x) = ? lo...

Bernstein's polynomials for convex functions and related results

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

Hyperbolic Polynomials and Spectral Order

bernstein's polynomials for convex functions and related results

in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.