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    Department of Systems Engineering and Engineering Management

                       The Chinese University of Hong Kong

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Date: Thursday, April 18, 4:30 pm – 5:30 pm

Venue: ERB 513, The Chinese University of Hong Kong

Title: Levenberg-Marquardt-type Methods for Bilevel Optimization

Speaker: Prof. Alain Zemkoho, University of Southampton

Abstract:

We consider the bilevel optimization problem in a very general setting, where the follower (or lower-level player) is free to choose whatever optimal solution that they want if their optimal solution set is not necessarily unique under some choices of the leader (or upper-level player). As it is well-known in the literature, this framework gives rise to the optimistic and pessimistic bilevel optimization problems, as tractable decision-making setups. In this talk, we consider both the optimistic and pessimistic scenarios of the problem and use the lower-level optimal value function reformulation to transform the follower’s problem into inequality constraints. We then discuss approaches to write necessary optimality conditions of these problems, which are amenable to tractable numerical methods. It turns out that in each case, these optimality conditions can be rewritten as overdetermined or squared systems of equations. We will therefore discuss smoothing and nonsmooth-types Levenberg-Marquardt methods to solve these equations and report on the very promising numerical results obtained.

Biography:

Alain is an associate professor in operational research at the School of Mathematical Sciences within the University of Southampton (UK), where he is affiliated to the OR Group and CORMSIS. Prior to joining the University of Southampton, Alain was a Research Fellow at the University of Birmingham (UK) and had previously worked as a Research Associate at the Technical University of Freiberg (Germany). He is an Alexander von Humboldt Experienced Fellow 2024-2026, a Fellow of the Alan Turing Institute for Data Science and Artificial Intelligence 2019-2023, a Fellow of the Institute of Mathematics & Its Applications, and a Fellow of the Higher Education Academy.

Everyone is welcome to attend the talk!

SEEM-5202 Website: http://seminar.se.cuhk.edu.hk

Email: seem5202@se.cuhk.edu.hk