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 these types of methods and relevant challenges. We will conclude the talk with some promising numerical results. 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.

Join Zoom Meeting
https://umich.zoom.us/j/95524251106?pwd=TUN5SnlVQzB5bGRtejZRU2NhVXpJUT09

Meeting ID: 955 2425 1106
Passcode: 491904 Speaker(s): Alain Zemkoho (University of Southampton, UK)