A Julia package for bilevel optimization problems

Abstract

Mathematical optimization is the discipline dealing with the determination of the best (or almost best) decision with respect to a specific cost function and to a set of constraints on the decision. Bilevel optimization is a class of mathematical optimization problems with the optimality conditions of a lower-level problem embedded in the constraints. BilevelOptimization.jl is a toolbox built on top of the JuMP.jl ecosystem for mathematical optimization (Dunning, Huchette, & Lubin, 2017). Bilevel optimization is used to tackle various problems in areas such as power systems, security applications, network design or market equilibria. See Dempe (2018) for an overview of applications and recent formulations and theoretical progress.

DynamicOED.jl: A Julia package for solving optimum experimental design problems

“…Martensen et al (2024). DynamicOED.jl: A Julia package for solving optimum experimental design problems.…”

The Effectiveness of Bilevel Optimization in Large-Scale Power Systems Problems: A Bilevel Optimization Toolbox, a Framework for Application-Driven Learning, and a Market Simulator

“…Regarding similar works, [110] provided great motivation and a nice first step to tackle bilevel models in Julia. However, it is incomplete as a modeling framework due to the strong limitations associated with the modeling Similar to other interfaces, BilevelJuMP.jl is also capable of reformulating bilevel problems and exporting the model to existing external solvers.…”

“…The Julia [41] package BilevelOptimization.jl [110] provides a very simple interface for Bilevel modeling in JuMP [37,111]. Still, the interface remains very basic.…”