Geometry of convex sets arising from hyperbolic polynomials

hyperbolic polynomials;continuous optimization;Combinatorics and Optimization

Myklebust, Tor Gunnar Josefsson Jay

University of Waterloo

关键词: hyperbolic polynomials;    continuous optimization;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3960/1/thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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.