Stephan Dempe is a leading expert in the field of bilevel optimization. He studied mathematics at Karl-Marx-Stadt University of Technology (GDR) where he received his diploma degree in 1981. Until 1995 he stayed there and successfully completed his PhD under supervision of Knut Richter as well as his habilitation in the working group of Klaus Beer. Based on research stays at the Belorussian State University Minsk (USSR) in 1982 and at the Leningrad State University (USSR) in 1988, Stephan gained international scientific expertice. After a short academic stay in Leipzig (Germany) he was appointed full professor at Technical University “Bergakademie” Freiberg (Germany). Stephan authored, co-authored, or edited approximately 150 papers, book chapters, and books mostly concerned with theoretical and numerical issues in mathematical bilevel optimization. During his long career, Stephan supervised 18 PhD students. He retired in autumn 2022.
Transformation of bilevel optimization problems into single level ones
Bilevel optimization problems are hierarchical problems where the second (or lower-level) problem is a parametric optimization problem. For solving it, we need to transform it into a single-level problem. This can be realized using various approaches: we can replace the lower-level problem using its Karush-Kuhn-Tucker optimality conditions, apply Lagrange, Wolfe as well as Mond–Weir duality, or formulate a new constraint involving its optimal value function. The presentation deals with relations between the bilevel optimization problem and its single-level transformations, and also properties of the latter problems.
Ivana Ljubić received her PhD in computer science at Vienna University of Technology, where she has been supervised by Petra Mutzel and Ulrich Pferschy, in 2004 and her habilitation in operations research at the University of Vienna in 2013. She stayed at the University of Vienna as an associate professor until 2015. Since 2015 Ivana is employed at ESSEC Business School in Paris, where she has been promoted to a full professor of operations research in 2016. Her academic career is adorned with several international research stays in Chile, France, Germany, Italy, and the Unites States. Her research has been published in more than 100 papers and book chapters, and focuses on diverse topics of operations research including applications of bilevel optimization and the development of exact methods for discrete bilevel optimization.
Bilevel optimization under uncertainty
Significant algorithmic advances in the field of computational bilevel optimization allow us to solve much larger and also more complicated problems today compared to what was possible two decades ago. This results in more and more challenging bilevel problems that researchers try to solve today. In this talk, we will focus on one of these more challenging classes of bilevel problems: bilevel optimization under uncertainty. We will discuss classical ways of addressing uncertainties in bilevel optimization using stochastic or robust techniques. Moreover, the sources of uncertainty in bilevel optimization can be much richer than for usual, single-level problems, since not only the problem’s data can be uncertain but also the (observation of the) decisions of the two players can be subject to uncertainty. Thus, we will also discuss bilevel optimization under limited observability, the area of problems considering only near-optimal decisions, and intermediate solution concepts between the optimistic and pessimistic cases.
The talk is based on joint work with Yasmine Beck and Martin Schmidt.
Martin Schmidt studied mathematics at the Leibniz University Hannover (Germany) and received his diploma in 2008. Afterward, he got his PhD at the Leibniz University Hannover in 2013 under the supervision of Marc Steinbach. In 2018, Martin became a junior professor at the Friedrich-Alexander-University Erlangen-Nürnberg (Germany). In 2019, he moved to Trier, where he is now a full professor for nonlinear optimization. Martin wrote approximately 100 papers and book chapters dealing with diverse aspects of continuous and mixed-integer optimization with a special emphasis on bilevel optimization and applications addressing energy markets.
Matchmaking bilevel and Γ-robust optimization
Robust optimization is a prominent approach in optimization to deal with uncertainties in the data of the optimization problem by hedging against the worst-case realization of the uncertain event. Doing this usually leads to a multilevel structure of the mathematical formulation that is very similar to what we are used to consider in bilevel optimization. Hence, these two fields are closely related but the study of their combination is still in its infancy. In this talk, we show how branch-and-cut methods can be derived for solving discrete bilevel problems in which the follower tackles uncertainties in a Γ-robust way. Moreover, we discuss structural results showing that the Γ-robust bilevel problem can be solved by solving a polynomial set of nominal, i.e., certain, bilevel problems. By doing so, we generalize the famous result by Bertsimas and Sim for combinatorial optimization to combinatorial bilevel optimization.
The talk is based on joint work with Yasmine Beck and Ivana Ljubić.
Jane Juan Ye
Jane J. Ye is a professor at the University of Victoria (British Columbia, Canada) working in the areas of nonsmooth optimization and variational analysis with a strong focus on bilevel optimization and its applications. She received her bachelor degree in mathematics back in 1982 from the Xiamen University (Fujian, China) before moving to the Dalhousie University Halifax (Nova Scotia, Canada) in 1984 where she completed her PhD in 1990 under supervision of Michael A. H. Dempster. Afterwards, Jane became a postdoctoral fellow at the Université de Montréal (Québec, Canada) under supervision of Francis H. Clarke. In 1992, she moved to the University of Victoria (British Columbia, Canada) for an assistant professorship which has been turned into a full professorship in 2002. Jane received the Krieger-Nelson Prize of the Canadian Mathematical Society in 2015. She authored or coauthored more than 100 papers and book chapters dealing with the theoretical and numerical treatment of continuous optimization problems. Her special interest lies in complementarity-type and bilevel optimization.
Recent developments in solving bilevel programming problems
A bilevel optimization problem is a sequence of two optimization problems where the constraint region of the upper-level problem is determined implicitly by the solution set to the lower-level problem. It can be used to model a two-level hierarchical system where the two decision makers have different objectives and make their decisions on different levels of hierarchy. Recently, more and more applications including those in machine learning have been modeled as bilevel optimization problems. In this talk, I will report some recent developments in optimality conditions and numerical algorithms for solving this class of very difficult optimization problems.