Geometry of convex sets arising from hyperbolic polynomials
Loading...
Date
2008-09-09T15:31:05Z
Authors
Myklebust, Tor Gunnar Josefsson Jay
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials.
We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning polynomials in a single variable, as well as presenting a few more modern results about them. We then discuss the theory of hyperbolic polynomials in several variables and their associated hyperbolicity cones. We survey various ways to build and decompose hyperbolic cones and we prove that every nontrivial hyperbolic cone is the intersection of its derivative cones. We conclude with a brief discussion of the set of extreme rays of a hyperbolic cone.
Description
Keywords
hyperbolic polynomials, continuous optimization