Invited Session Fri.3.H 2036

Friday, 15:15 - 16:45 h, Room: H 2036

Cluster 4: Conic programming [...]

Algebraic geometry and conic programming III


Chair: Markus Schweighofer and Lek-Heng Lim



Friday, 15:15 - 15:40 h, Room: H 2036, Talk 1

Caroline Uhler
Maximum likelihood estimation in Gaussian graphical models from the perspective of convex algebraic geometry


We study multivariate normal models that are described by linear
constraints on the inverse of the covariance matrix. Maximum
likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. We examine these problems at the interface of statistics and conic optimization from the perspective of convex algebraic geometry.



Friday, 15:45 - 16:10 h, Room: H 2036, Talk 2

Thorsten Theobald
Containment problems for polytopes and spectrahedra

Coauthors: Kai Kellner, Christian Trabandt


Spectrahedra are the feasible regions of semidefinite
programs. In this talk we study the computational
question(s) whether a given polytope or spectrahedron
SA (as given by a linear matrix pencil A(x)) is
contained in another one SB.
Our results both concern the computational complexity
(extending results on the polytope/polytope-case by
Gritzmann and Klee) as well as sufficient conditions
to certify containedness (whose study was initiated
by Ben-Tal, Nemirovski and Helton, Klep, McCullough).


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