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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. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The authors were partially supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The work of A. Street was also partially supported by Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). The work was partially funded by the project P&D ANEEL PD-00403-0050/2020 sponsored by ENGIE BRASIL ENERGIA S.A. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0135) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0135). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

We introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work of A. Sharma on DiffOpt.jl was funded by the Google Summer of Code program through NumFocus. M. Besançon was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research [Grant 05M14ZAM, 05M20ZBM]. J. Dias Garcia was supported in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. B. Legat was supported by a BAEF Postdoctoral Fellowship, the NSF [Grant OAC-1835443], and the ERC Adv. [Grant 885682]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0283), as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0283). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms. Stochastic programming models can be efficiently formulated using an expressive syntax, and models can be instantiated, inspected, and analyzed interactively. The framework scales seamlessly to distributed environments. Small instances of a model can be run locally to ensure correctness, whereas larger instances are automatically distributed in a memory-efficient way onto supercomputers or clouds and solved using parallel optimization algorithms. These structure-exploiting solvers are based on variations of the classical L-shaped, progressive-hedging, and quasi-gradient algorithms. We provide a concise mathematical background for the various tools and constructs available in the framework along with code listings exemplifying their usage. Both software innovations related to the implementation of the framework and algorithmic innovations related to the structured solvers are highlighted. We conclude by demonstrating strong scaling properties of the distributed algorithms on numerical benchmarks in a multinode setup. Summary of Contribution: This paper presents StochasticPrograms.jl, an open-source framework for stochastic programming implemented in the Julia programming language. The framework includes an expressive syntax for formulating stochastic programming models as well as versatile analysis tools and parallel optimization algorithms. The framework will prove useful to researchers, educators, and industrial users alike. Researchers will benefit from the readily extensible open-source framework, in which they can formulate complex stochastic models or quickly typeset and test novel optimization algorithms. Educators of stochastic programming will benefit from the clean and expressive syntax. Moreover, the framework supports analysis tools and stochastic programming constructs from classical theory and leading textbooks. We strongly believe that the StochasticPrograms.jl framework can reduce the barrier to entry for incoming practitioners of stochastic programming. Industrial practitioners can make use of StochasticPrograms.jl to rapidly formulate complex models, analyze small instances locally, and then run large-scale instances in production. In doing so, they get distributed capabilities for free without changing the code and access to well-tested state-of-the-art implementations of parallel structure-exploiting solvers. As the framework is open-source, anyone from these target audiences can contribute with new functionality to the framework. In conclusion, by providing both an intuitive interface for new users and an extensive development environment for expert users, StochasticPrograms.jl has strong potential to further the field of stochastic programming. [ABSTRACT FROM AUTHOR]

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before. [ABSTRACT FROM AUTHOR]