Structural Convex Optimization: snapshot of the development

In this lecture we present the current status of research in one specific
field of structural convex optimization. Firstly, we describe some
applications related to random permutations and their use in machine
scheduling. We show that the similar objects arise in switching linear
systems. Moreover, for some nontrivial sets of positive matrices they can
help to find exact values of the joint spectral radius. Finally, we describe
the recent progress in algorithmic aspects related to the development of
corresponding long-step infeasible-start interior-point methods.

BIO

Yurii Nesterov, professor at Center for Operations Research and Econometrics
(CORE), Catholic University of Louvain (UCL), Louvain-la-Neuve, Belgium.

Author of 4 monographs and more than 70 refereed papers in the leading
optimization journals. Winner of the triennial Dantzig Prize 2000 awarded by
SIAM and Mathematical Programming Society for a research having a major
impact on the field of mathematical programming.

The main direction of his research is the development of efficient numerical
methods for convex and nonconvex optimization problems supported by the
global complexity analysis. The most important results are obtained for
general interior-point methods (theory of self-concordant functions), fast
gradient methods (smoothing technique) and global complexity analysis of the
second-order schemes (cubic regularization of the Newton's method).