Optimization

• MathOptInterface.jl: An abstraction layer for mathematical optimization solvers.

• JuMP.jl: Domain-specific modeling language for mathematical optimization built on top of MathOptInterface.

• SumOfSquares.jl: Sum of Squares restriction and Moment relaxation for PolyJuMP.jl: JuMP extension for polynomial variables and polynomial nonnegativity constraints.

• SetProg.jl: JuMP extension for set variables and inclusion constraints.

• DiffOpt.jl: Implicit differentiation of the solution of JuMP parametric optimization programs with respect to the parameters.

• ArrayDiff.jl: Tensor AD for JuMP.

• GenOpt.jl: Pack groups of similar constraints of sum of similar terms into lightweight generators. This representation can then be used by ExaModels to accelerate the Automatic Differentiation on GPU.

• LowRankOpt.jl: Low-rank constraints and Burer-Monteiro formulation.

• ComplementOpt.jl: Reformulation of complementarity constraints.

Utilities

• JuliaPolyhedra:

  • Polyhedra.jl: Polyhedral computation framework with support for

    • CDD,

    • LRS,

    • QHull,

    • ConvexHull.jl and

    • PORTA.

• JuliaAlgebra:

  • MultivariatePolynomials.jl: Interface for multivariate polynomials with two implementations:

    • DynamicPolynomials.jl and

    • TypedPolynomials.jl.

  • MultivariateBases.jl: Bases for multivariate polynomials.

  • SemialgebraicSets.jl: Representation of algebraic sets and basic semialgebraic sets, groebner basis computation and solvers for algebraic systems.

  • MultivariateMoments.jl: Extraction of atomic measures from moment matrices.

• MutableArithmetics.jl: Interface for efficient arithmetics on mutable types

• HybridSystems.jl: Hybrid systems implementations.

High level toolbox

• EntropicCone.jl: Approximation of the Entropic Cone and optimization over it.

• SwitchOnSafety.jl: Computation of invariant sets for hybrid systems.

• Dionysos.jl: Optimal control on hybrid systems