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HugeOPT: Krylov accelerated splitting methods for huge-scale network optimization. 01/10/2023 - 30/09/2027

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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  • Research Project