COPT.jl

COPT.jl is a wrapper for the COPT (Cardinal Optimizer), a mathematical optimization solver for large-scale optimization problems.

COPT includes high-performance solvers for LP, MIP, SOCP, convex QP/QCP and SDP.

License

COPT.jl is licensed under the MIT license.

The underlying solver is a closed-source commercial product for which you must obtain a license.

When COPT is upgraded to a newer version, you may see an error message such as ERROR: COPT error 4: Unable to create COPT environment, which indicates that you will need to reapply and upgrade your COPT license files as well.

Installation

Install COPT using the Julia package manager

import Pkg
Pkg.add("COPT")

When there is no local version of COPT installed, installing COPT.jl will automatically download the necessary solver binaries.

Without a license, you can solve small models for non-commercial purpose. We strongly recommend that you apply for a license by following the link above.

Note

MacOS Apple M1/ARM: on MacOS with Apple M1 chips, Intel based programs can run via Rosetta. When you installed the COPT binaries manually, then please make sure that the COPT build matches the Julia build. We recommend the Intel based COPT and Julia build, as the Apple M1/ARM build of Julia is experimental.

Use with JuMP

To use COPT with JuMP, use COPT.Optimizer:

using JuMP
using COPT
model = Model(COPT.Optimizer)
@variable(model, x >= 0)
@variable(model, 0 <= y <= 3)
@objective(model, Min, 12x + 20y)
@constraint(model, c1, 6x + 8y >= 100)
@constraint(model, c2, 7x + 12y >= 120)
print(model)
optimize!(model)
@show termination_status(model)
@show primal_status(model)
@show dual_status(model)
@show objective_value(model)
@show value(x)
@show value(y)
@show shadow_price(c1)
@show shadow_price(c2)

To use the semidefinite programming solver in COPT with JuMP, use COPT.ConeOptimizer:

using JuMP
using COPT
using LinearAlgebra
model = Model(COPT.ConeOptimizer)
C = [1.0 -1.0; -1.0 2.0]
@variable(model, X[1:2, 1:2], PSD)
@variable(model, z[1:2] >= 0)
@objective(model, Min, C ⋅ X)
@constraint(model, c1, X[1, 1] - z[1] == 1)
@constraint(model, c2, X[2, 2] - z[2] == 1)
optimize!(model)
@show termination_status(model)
@show primal_status(model)
@show dual_status(model)
@show objective_value(model)
@show value.(X)
@show value.(z)
@show shadow_price(c1)
@show shadow_price(c2)