JuliaOpt

Optimization packages for the Julia language.

What is Julia?

“Julia is a high-level, high-performance 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.

What is JuliaOpt?

The JuliaOpt GitHub organization is home to a number of optimization-related packages written in Julia. Its purpose is to facilitate collaboration among developers of a tightly integrated set of packages for mathematical optimization.

Overview: presentation and workshop from JuliaCon 2015
Code: github.com/JuliaOpt
Forum: Discourse
Old Mailing list: julia-opt
Case study: Computing in Operations Research using Julia, INFORMS Journal on Computing. [PDF]

Overview of Packages

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)

Solvers

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	Linear / Quadratic	Conic	Smooth	Nonconvex	Integer	License
Key: Linear/Quadratic = Supports Linear Programming possibly with the addition of quadratic objectives or constraints. Convex conic = Supports Second-order Cone Programming or Semidefinite Programming or exponential cones. Convex smooth = Supports constrained derivative-based Nonlinear Programming with convex constraints and objective functions Nonconvex = Supports general nonconvex nonlinear programming. Integer = Supports integer-constrained variables, e.g., Integer Programming. cb = Supports Integer Programming callbacks. License: Open = Open Source Comm. = Commercial a = Commercial, but provides free academic license
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
SDPA (.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