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Abstract: Hyperbolic polynomials have their origins in partial differential 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. The function F (x) = \Gamma log p(x) is a logarithmically homogeneous self--concordant barrier function for the hyperbolicity cone with barrier parameter equal to the degree of p. The function F (x) possesses... (Update)
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BibTeX entry: (Update)
@misc{ ler-hyperbolic,
author = "Osman Güler",
title = "Hyperbolic Polynomials and Interior Point Methods for Convex Programming",
url = "citeseer.ist.psu.edu/26205.html" }
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2 Notes on the efficiency of the barrier method (context) - Renegar - 1992
2 Private communication (context) - Renegar - 1994
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