Title:

Newton-type methods for bilevel optimization

Abstract:

A bilevel optimization problem is a special class of optimization problem partly constrained by another optimization problem. The problem can be traced back to the habilitation thesis of German economist Heinrich von Stackelberg, which was completed in 1934. Hence, the problem is referred to by economists and game theorists as a Stackelberg game. The bilevel optimization problem, which clearly has a hierarchical structure with two levels of decision-making, respectively controlled by a leader and a follower, represents a powerful tool for modelling the interactions between various engineering, economic, and human systems. The problem was introduced in the field of optimization in the early 1970s and interest in the subject has grown exponentially since then, driven largely by the wide range of applications. Initial works on the optimization side were significantly influenced by developments in the closely related area of mathematical programs with equilibrium or complementarity constraints. Recently though, the more natural transformation known as the lower-level value function reformulation has also been at the center of attentions, and will represent the main focus of our analysis in this talk. In particular, we will discuss some recent attempts to design Newton-type methods for bilevel optimization problems, covering the theoretical framework for this type of methods and relevant challenges. We will start the talk with some motivating applications and conclude it with some promising numerical results showing the potential of Newton-type methods. This talk is based on the papers [1, 2, 3].

References

[1] Fischer, A., Zemkoho, A.B. and Zhou, S., 2021. Semismooth Newton-type method for bilevel optimization: Global convergence and extensive numerical experiments. Optimization Methods and Software, doi:10.1080/10556788.2021.1977810

[2] Fliege, J., Tin, A. and Zemkoho, A., 2021. Gauss–Newton-type methods for bilevel optimization. Computational Optimization and Applications, 78(3), pp.793-824.

[3] Zemkoho, A.B. and Zhou, S., 2021. Theoretical and numerical comparison of the Karush–Kuhn–Tucker and value function reformulations in bilevel optimization. Computational Optimization and Applications, 78(2), pp.625-674.

Biography:

Alain Zemkoho is an Associate Professor at the School of Mathematical Sciences within the University of Southampton where he is affiliated to the Operational Research Group and CORMSIS. Prior to joining the University of Southampton, he was a Research Fellow at the University of Birmingham and had previously worked as a Research Associate at the Technical University of Freiberg (Germany). He is a Fellow of the Alan Turing Institute for Data Science and Artificial Intelligence, a Fellow of the Institute of Mathematics & Its Applications, and a Fellow of the UK Higher Education Academy. His research interests are around the theory and methods for nonconvex, nonsmooth, and bilevel optimization, as well as their applications, including in machine learning, transportation, healthcare and medicine. 

 

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