BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia

Joaquim Dias Garcia (), Guilherme Bodin () and Alexandre Street ()
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Joaquim Dias Garcia: PSR, Rio de Janeiro, Rio de Janeiro 22250-040, Brazil; LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
Guilherme Bodin: PSR, Rio de Janeiro, Rio de Janeiro 22250-040, Brazil; LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil
Alexandre Street: LAMPS at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Rio de Janeiro 22451-900, Brazil

INFORMS Journal on Computing, 2024, vol. 36, issue 2, 327-335

Abstract: In this paper, we present BilevelJuMP.jl, a new Julia package to support bilevel optimization within the JuMP framework. The package is a Julia library that enables the user to describe both upper and lower-level optimization problems using the JuMP algebraic syntax. Because of the generality and flexibility that our library inherits from JuMP’s syntax, our package allows users to model bilevel optimization problems with conic constraints in the lower level and all constraints supported by JuMP in the upper level including conic, quadratic, and nonlinear constraints. Moreover, the models defined with the syntax from BilevelJuMP.jl can be solved by multiple techniques that are based on reformulations as mathematical programs with equilibrium constraints (MPEC). Manipulations on the original problem data are possible due to MathOptInterface.jl’s structures and Dualization.jl features. Hence, the proposed package allows quick modeling, deployment, and thereby experimenting with bilevel models based on off-the-shelf mixed-integer linear programming and nonlinear solvers.

Keywords: bilevel optimization; Julia; JuMP; algebraic modeling language; automatic reformulation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:36:y:2024:i:2:p:327-335

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