Inner approximation of convex cones via primal-dual ellipsoidal norms
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Date
2016-05-13
Authors
Xie, Miaolan
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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.
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Master Thesis