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.
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.
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.
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)