This Julia package allows us to specify a set of constraints on real-valued variables, given by inequalities, and rigorously calculate (inner and outer approximations to) the feasible set, i.e. the set that satisfies the constraints.
The package is based on interval arithmetic using the
IntervalArithmetic.jl package (co-written by the author),
in particular multi-dimensional IntervalBoxes (i.e. Cartesian products of one-dimensional intervals).
Documentation for the package is available here.
The best way to learn how to use the package is to look at the tutorial, available in the organisation webpage here.
ModelingToolkit can be used to conveniently define constraints, as described in the tutorial. However, that package is only compatible up to Julia version 1.9, and it needs to be installed manually and restricted to version 3. Later versions of ModelingToolkit or Julia are not compatible yet.
- David P. Sanders, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
- Applied Interval Analysis, Luc Jaulin, Michel Kieffer, Olivier Didrit, Eric Walter (2001)
- Introduction to the Algebra of Separators with Application to Path Planning, Luc Jaulin and Benoît Desrochers, Engineering Applications of Artificial Intelligence 33, 141–147 (2014)
Financial support is acknowledged from DGAPA-UNAM PAPIME grants PE-105911 and PE-107114, and DGAPA-UNAM PAPIIT grant IN-117214, and from a CONACYT-Mexico sabbatical fellowship. The author thanks Alan Edelman and the Julia group for hospitality during his sabbatical visit. He also thanks Luc Jaulin and Jordan Ninin for the IAMOOC online course, which introduced him to this subject.