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Convex Convex

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, GLPK, through the MathProgBase interface.

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

  • Detailed documentation and examples for Convex.jl can be found here
  • If you're running into bugs or have feature requests, please use the Github Issue Tracker.
  • For usage questions, please contact us via the JuliaOpt mailing list

Quick Example

Here's a quick example of code that solves a least-squares problem with inequality constraints

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

# 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!

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

# Get the optimal value

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

Citing this package

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

 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.