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.
JuliaOpt is an organization that brings together packages written in Julia that are related to optimization. All JuliaOpt packages should be highquality, documented, tested, support the main operating systems, and interact with each other.
JuliaOpt’s packages can be loosely grouped into two sets. The first set are standalone Julia packages:
Optim.jl: Implementations in Julia of standard optimization algorithms for unconstrained or boxconstrained problems such as BFGS, NelderMead, conjugate gradient, etc. (documentation/code)
LsqFit.jl: Leastsquares nonlinear curve fitting in Julia. (documentation/code)
The second set comprises modeling languages (red), external solver interfaces (purple), and an abstraction layer over the solvers (green), primarily for constrained optimization:
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)
MathProgBase  A standardized interface implemented by all solvers that allows code to remain solveragnostic. Used by JuMP and Convex.jl, but can be called by user code directly if a user doesn’t want to go through a modeling language, but wishes to remain solverindependent. (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}  
NLopt (.jl)  ✔  ✔  Open  
Ipopt (.jl)  ✔  ✔  ✔  Open  
Bonmin (via AmplNLWriter.jl)  ✔  ✔  ✔  ✔  Open  
Couenne (via AmplNLWriter.jl)  ✔  ✔  ✔  ✔  Open  
Artelys Knitro (.jl)  ✔  ✔  ✔  ✔  Comm. 