Using Julia interface for COPT (Cardinal Optimizer)

COPT (Cardinal Optimizer) is a mathematical optimization solver for large-scale optimization problems. It includes high-performance solvers for LP, MIP, SOCP, convex QP/QCP and SDP.

Prerequisite

COPT.jl requires Julia version 1.6 or above. Please apply for a free personal COPT license from COPT application page.

Installation

Please install JuMP and COPT Julia interface from Julia with:

import Pkg
Pkg.add("JuMP")
Pkg.add("COPT")

When there is no COPT installed, installing the COPT Julia interface 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.

Notes
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.

Quick check

When the installation is done, you should be able to build and solve an LP problem with:

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)

For solving SDP problems, you need to use COPT.ConeOptimizer in place of COPT.Optimizer:

using JuMP
using COPT
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)

Please refer to Getting started with JuMP for a quick introduction to writing and solving optimization models with JuMP. The model above is adapted from the introduction page.