Half-time seminar: 'Learning to accelerate large-scale optimization algorithms'

Supervisor: Jens Sjölund
External reviewer: Elias Jarlebring (KTH)

Summary: Solving large-scale optimization problems is ubiquitous in engineering and scientific computing. For practical applications similar optimization problems have to be solved repeatedly. However, classical algorithms and their convergence only depend on the function properties and usually do not take into account the distribution of problems of interest. In this half-time seminar we present methods developed to accelerate optimization problems coming from a specific distribution using machine learning techniques. The first problem class we consider is solving large-scale and sparse linear equation systems that typically get solved using Krylov subspace methods. We utilize the connections of graph neural networks and numerical linear algebra to learn a preconditioner for the equation system. The second problem we consider is solving regularized linear inverse problems. In particular, we accelerate an alternating minimization scheme for solving dictionary regularized CT reconstruction. We conclude the presentation with an outlook and future work.