Apostolos Chalkis will defend his PhD thesis via Zoom on Monday 20\/12 from 9.00 am until 11.00 am (EEST). If you want to join the presentation please send and email to send you the Zoom link.<\/p>\n\n\n\n
Thesis title: Efficient geometric random walks for high-dimensional sampling from convex bodies<\/p>\n\n\n\n
Abstract:
High-dimensional sampling is a fundamental problem with plenty of applications in science and engineering. Several problems are
computationally hard for general dimension, and therefore, a great effort has been devoted to randomized approximation algorithms based on sampling
to address those problems in polynomial time. In this thesis, I present algorithmic, complexity, and implementation results on the problem of
sampling points from a log-concave distribution restricted to a convex polytope \u2013the feasible region of a linear program\u2013 or a spectrahedron \u2013the
feasible region of a semidefinite program (SDP). I use those methods to address the problem of approximating the volume of convex bodies and
analyzing metabolic networks. Finally, I use sampling and develop new geometric and mathematical tools to address three important problems in
finance: (i) portfolio scoring, (ii) portfolio optimization, and (iii) crises detection in stock markets.<\/p>\n","protected":false},"excerpt":{"rendered":"