Show simple item record

dc.contributor.authorMyklebust, Tor Gunnar Josefsson Jay 15:31:05 (GMT) 15:31:05 (GMT)
dc.description.abstractThis 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.en
dc.publisherUniversity of Waterlooen
dc.subjecthyperbolic polynomialsen
dc.subjectcontinuous optimizationen
dc.titleGeometry of convex sets arising from hyperbolic polynomialsen
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages