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?

JuliaOpt is an organization that brings together packages written in Julia that are related to optimization. All JuliaOpt packages should be high-quality, documented, tested, support the main operating systems, and interact with each other.

• 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

JuMPConvex.jlMathProgBase.jlCbc.jlClp.jlCPLEX.jlECOS.jlGLPK.jlGurobi.jlIpopt.jlKNITRO.jlMosek.jlNLopt.jlSCS.jlXpress.jl Optim.jlLsqFit.jlCoinOptServices.jlAmplNLWriter.jl

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 box-constrained problems such as BFGS, Nelder-Mead, conjugate gradient, etc. (documentation/code)

• LsqFit.jl: Least-squares non-linear 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 solver-agnostic. 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 solver-independent. (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		Conic	Smooth
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
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.