Inner approximation of convex cones via primal-dual ellipsoidal norms

Master Thesis

Xie, Miaolan

University of Waterloo

关键词: Master Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/10474/1/Xie_Miaolan.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

We study ellipsoids from the point of view of approximating convex sets. Our focus ison finding largest volume ellipsoids with specified centers which are contained in certainconvex cones. After reviewing the related literature and establishing some fundamentalmathematical techniques that will be useful, we derive such maximum volume ellipsoidsfor second order cones and the cones of symmetric positive semidefinite matrices. Then wemove to the more challenging problem offinding a largest pair (in the sense of geometricmean of their radii) of primal-dual ellipsoids (in the sense of dual norms) with specifiedcenters that are contained in their respective primal-dual pair of convex cones.