UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Inner approximation of convex cones via primal-dual ellipsoidal norms

Thumbnail Image

Files

Xie_Miaolan.pdf (745.4 KB)

Date

2016-05-13

Authors

Xie, Miaolan

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

We study ellipsoids from the point of view of approximating convex sets. Our focus is on finding largest volume ellipsoids with specified centers which are contained in certain convex cones. After reviewing the related literature and establishing some fundamental mathematical techniques that will be useful, we derive such maximum volume ellipsoids for second order cones and the cones of symmetric positive semidefinite matrices. Then we move to the more challenging problem of finding a largest pair (in the sense of geometric mean of their radii) of primal-dual ellipsoids (in the sense of dual norms) with specified centers that are contained in their respective primal-dual pair of convex cones.

Description

Keywords

Master Thesis

LC Keywords

Citation

URI

http://hdl.handle.net/10012/10474

Collections

Theses
Combinatorics and Optimization