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 MathOptInterface. It also supports optimization with complex variables and coefficients.
Installation: julia> Pkg.add("Convex")
- Detailed documentation and examples for Convex.jl (stable | development version).
- If you're running into bugs or have feature requests, please use the Github Issue Tracker.
- For usage questions, please contact us via Discourse.
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, SCS.Optimizer)
# Check the status of the problem
problem.status # :Optimal, :Infeasible, :Unbounded etc.
# Get the optimal value
problem.optvalA number of examples can be found here. The basic usage notebook gives a simple tutorial on problems that can be solved using Convex.jl. All examples can be downloaded as a zip file from here.
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.