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Numerical Methods for Control and Games over Multiscale Agent-Based Models

Dante Kalise, Imperial College London

We will discuss different approximation techniques for the solution of optimal control problems and games where the governing dynamics are give by multiscale models. We will start by reviewing some classical results concerning the solution of nonlinear optimal control problems, illustrating some of the difficulties which arise when the number of agents increases. This will lead us to mean-field and multiscale models, for which we will study their approximation within the framework provided by PDE-constrained optimization. Finally, starting from mean-field type control problems, we will move towards the numerical solution of mean field games.

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Short Bio:

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Dante Kalise is Imperial College Research Fellow at the Department of Mathematics, Imperial College London, UK. Dante received a BSc in Engineering Mathematics and a MSc in Electronic Engineering from the Federico Santa María University (Valparaíso, Chile) and a PhD in Mathematics from the University of Bergen (Norway). He has previously held postdoctoral appointments at La Sapienza University (Rome, Italy), the Radon Institute for Computational and Applied Mathematics in (Linz, Austria) and visiting positions in Oslo, Trento, and Bayreuth. His research areas lie in Scientific Computing, Model-driven Optimisation and Control,  and Agent-based Modelling. 

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