Abstract
Efficiently solving huge-scale optimization problems is undoubtedly very important in science and
technology. Many optimization problems can be described using some underlying network structure.
For example, the optimal assignment of a crew to a given flight schedule can be formulated as an
optimization problem over a very large graph. Similarly, constraint based modelling of biochemical
networks also leads to optimization problems with millions of unknowns. A network structure
typically induces useful structure in the constraints, which then of course can be exploited by using
suitably chosen linear algebra techniques. Current off-the-shelf software is not able to efficiently
solve such problems when the number of variables is very large, especially when the objective
function is nonconvex and possibly contains a nonsmooth term. Hence, there is a need to develop
high-performance structure exploiting algorithms. In this project we aim to develop a wide range of
efficient optimization algorithms for both convex and nonconvex problems, possibly containing a
nonsmooth term in the objective function, by exploiting structure that arises from the networks.
High-performance implementations of the resulting algorithms will be made available in an open-
source software package such that non-expert practitioners can easily them.
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