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MathOptInterface: a data structure for mathematical optimization problems

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arxiv 2002.03447 v3 pith:KUYVHXNC submitted 2020-02-09 math.OC

Benoit Legat , Oscar Dowson , Joaquim Dias Garcia , Miles Lubin This is my paper · ORCID
classification math.OC
keywords mathoptinterfacedatamathematicaloptimizationproblemsautomatedgeneraljump
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We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining pre-defined 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.

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  1. Robust Bilevel Optimization for Near-Optimal Lower-Level Solutions

    math.OC 2019-08 conditional novelty 7.0 of 10

    A near-optimal robust bilevel problem protects upper-level feasibility against approximately optimal follower responses, with an exact MILP reformulation for linear-linear instances.

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