Convex.jl

Convex.jl is a Julia package for Disciplined Convex Programming. Convex.jl can solve linear programs, mixed-integer linear programs, and DCP-compliant convex programs using a variety of solvers, including Mosek, Gurobi, ECOS, SCS, and GLPK, through the MathProgBase interface. It also supports optimization with complex variables and coefficients.

Installation: julia> Pkg.add("Convex")

• Detailed documentation and examples for Convex.jl (stable | latest).
• If you're running into bugs or have feature requests, please use the Github Issue Tracker.
• For usage questions, please contact us via Discourse.

Quick Example

To run this example, first install Convex and at least one solver, such as SCS:

using Pkg
Pkg.add("Convex")
Pkg.add("SCS")

Now let's solve a least-squares problem with inequality constraints.

# Let us first make the Convex.jl module available
using Convex, SCS

# Generate random problem data
m = 4;  n = 5
A = randn(m, n); b = randn(m, 1)

# Create a (column vector) variable of size n x 1.
x = Variable(n)

# The problem is to minimize ||Ax - b||^2 subject to x >= 0
# This can be done by: minimize(objective, constraints)
problem = minimize(sumsquares(A * x - b), [x >= 0])

# Solve the problem by calling solve!
solve!(problem, SCSSolver())

# Check the status of the problem
problem.status # :Optimal, :Infeasible, :Unbounded etc.

# Get the optimal value
problem.optval

More Examples

A number of examples can be found here. The basic usage notebook gives a simple tutorial on problems that can be solved using Convex.jl. Many use cases of the package in complex-domain optimization can be found here.

Note: many of the examples are currently outdated (August 2019). Pull requests to update them are greatly appreciated!

Citing this package

If you use Convex.jl for published work, we encourage you to cite the software using the following BibTeX citation:

@article{convexjl,
 title = {Convex Optimization in {J}ulia},
 author ={Udell, Madeleine and Mohan, Karanveer and Zeng, David and Hong, Jenny and Diamond, Steven and Boyd, Stephen},
 year = {2014},
 journal = {SC14 Workshop on High Performance Technical Computing in Dynamic Languages},
 archivePrefix = "arXiv",
 eprint = {1410.4821},
 primaryClass = "math-oc",
}

Convex.jl was previously called CVX.jl.