Optimization packages for the Julia language.
“Julia is a highlevel, highperformance dynamic programming language for technical computing”. It is free (open source) and supports Windows, OSX, and Linux. It has a familiar syntax, works well with external libraries, is fast, and has advanced language features like metaprogramming that enable interesting possibilities for optimization software.
The JuliaOpt GitHub organization is home to a number of optimizationrelated packaged written in Julia. Its purpose is to facilitate collaboration among developers of a tightly integrated set of packages for mathematical optimization.
JuliaOpt’s packages currently all revolve around the MathProgBase abstraction layer (green). Above the abstraction layer we have modeling languages (red), and below external solver interfaces (purple). The modeling languages in JuliaOpt are:
JuMP: An algebraic modeling language for linear, quadratic, and nonlinear constrained optimization problems embedded in Julia. Generates models as quick as commercial modeling tools and supports advanced features like solver callbacks. (documentation, code)
Convex.jl: An algebraic modeling language for disciplined convex programming embedded in Julia. (documentation, code)
JuliaOpt provides wrappers for a wide variety of solvers. The following table summarizes the forms supported by the modeling languages and solvers. Note that the capabilities marked in the table represent those of the Julia package, not necessarily the capabilities of the solver itself.
Linear / Quadratic 
Convex  Nonconvex  Integer  License  

Modeling Tool  Conic  Smooth  
Key:


JuMP  ✔  ✔  ✔  ✔  ✔  Open 
Convex.jl  ✔  ✔  ✔  Open  
Solver  
CDD (.jl)  ✔  Open  
Clp (.jl)  ✔  Open  
Cbc (.jl)  ✔  ✔  Open  
GLPK (.jl)  ✔  ✔^{cb}  Open  
CSDP (.jl)  ✔  ✔  Open  
ECOS (.jl)  ✔  ✔  Open  
SCS (.jl)  ✔  ✔  Open  
CPLEX (.jl)  ✔  ✔  ✔^{cb}  Comm.^{a}  
Gurobi (.jl)  ✔  ✔  ✔^{cb}  Comm.^{a}  
FICO Xpress (.jl)  ✔  ✔  ✔  Comm.^{a}  
Mosek (.jl)  ✔  ✔  ✔  ✔  Comm.^{a}  
Pajarito.jl  ✔  ✔  ✔  ✔  Open  
NLopt (.jl)  ✔  ✔  Open  
Ipopt (.jl)  ✔  ✔  ✔  Open  
Bonmin (via AmplNLWriter.jl)  ✔  ✔  ✔  ✔  Open  
Couenne (via AmplNLWriter.jl)  ✔  ✔  ✔  ✔  Open  
Artelys Knitro (.jl)  ✔  ✔  ✔  ✔  Comm.  
SCIP (.jl)  ✔  ✔  ✔  ✔  ✔^{cb}  Comm.^{a} 