Ipopt.jl is a wrapper for the Ipopt solver.

This wrapper is maintained by the JuMP community and is not a COIN-OR project.

Ipopt.jl is licensed under the MIT License.

The underlying solver, coin-or/Ipopt, is licensed under the Eclipse public license.

Install Ipopt.jl using the Julia package manager:

import Pkg
Pkg.add("Ipopt")

In addition to installing the Ipopt.jl package, this will also download and install the Ipopt binaries. You do not need to install Ipopt separately.

To use a custom binary, read the Custom solver binaries section of the JuMP documentation.

For details on using a different linear solver, see the Linear Solvers section below. You do not need a custom binary to change the linear solver.

You can use Ipopt with JuMP as follows:

using JuMP, Ipopt
model = Model(Ipopt.Optimizer)
set_attribute(model, "max_cpu_time", 60.0)
set_attribute(model, "print_level", 0)

The Ipopt optimizer supports the following constraints and attributes.

List of supported objective functions:

• MOI.ObjectiveFunction{MOI.ScalarAffineFunction{Float64}}
• MOI.ObjectiveFunction{MOI.ScalarQuadraticFunction{Float64}}
• MOI.ObjectiveFunction{MOI.VariableIndex}

List of supported variable types:

• MOI.Reals

List of supported constraint types:

• MOI.ScalarAffineFunction{Float64} in MOI.EqualTo{Float64}
• MOI.ScalarAffineFunction{Float64} in MOI.GreaterThan{Float64}
• MOI.ScalarAffineFunction{Float64} in MOI.LessThan{Float64}
• MOI.ScalarQuadraticFunction{Float64} in MOI.EqualTo{Float64}
• MOI.ScalarQuadraticFunction{Float64} in MOI.GreaterThan{Float64}
• MOI.ScalarQuadraticFunction{Float64} in MOI.LessThan{Float64}
• MOI.VariableIndex in MOI.EqualTo{Float64}
• MOI.VariableIndex in MOI.GreaterThan{Float64}
• MOI.VariableIndex in MOI.LessThan{Float64}

List of supported model attributes:

• MOI.BarrierIterations
• MOI.NLPBlock
• MOI.NLPBlockDualStart
• MOI.Name
• MOI.ObjectiveSense
• MOI.SolveTimeSec

Supported options are listed in the Ipopt documentation.

Ipopt provides a callback that can be used to log the status of the optimization during a solve. It can also be used to terminate the optimization by returning false. Here is an example:

using JuMP, Ipopt, Test
model = Model(Ipopt.Optimizer)
set_silent(model)
@variable(model, x >= 1)
@objective(model, Min, x + 0.5)
x_vals = Float64[]
function my_callback(
   alg_mod::Cint,
   iter_count::Cint,
   obj_value::Float64,
   inf_pr::Float64,
   inf_du::Float64,
   mu::Float64,
   d_norm::Float64,
   regularization_size::Float64,
   alpha_du::Float64,
   alpha_pr::Float64,
   ls_trials::Cint,
)
   push!(x_vals, callback_value(model, x))
   @test isapprox(obj_value, 1.0 * x_vals[end] + 0.5, atol = 1e-1)
   # return `true` to keep going, or `false` to terminate the optimization.
   return iter_count < 1
end
MOI.set(model, Ipopt.CallbackFunction(), my_callback)
optimize!(model)
@test MOI.get(model, MOI.TerminationStatus()) == MOI.INTERRUPTED
@test length(x_vals) == 2

See the Ipopt documentation for an explanation of the arguments to the callback. They are identical to the output contained in the logging table printed to the screen.

To access the current solution and primal, dual, and complementarity violations of each iteration, use Ipopt.GetIpoptCurrentViolations and Ipopt.GetIpoptCurrentIterate. The two functions are identical to the ones in the Ipopt C interface.

Ipopt.jl wraps the Ipopt C interface with minimal modifications.

A complete example is available in the test/C_wrapper.jl file.

For simplicity, the five callbacks required by Ipopt are slightly different to the C interface. They are as follows:

"""
   eval_f(x::Vector{Float64})::Float64

Returns the objective value `f(x)`.
"""
function eval_f end

"""
   eval_grad_f(x::Vector{Float64}, grad_f::Vector{Float64})::Nothing

Fills `grad_f` in-place with the gradient of the objective function evaluated at
`x`.
"""
function eval_grad_f end

"""
   eval_g(x::Vector{Float64}, g::Vector{Float64})::Nothing

Fills `g` in-place with the value of the constraints evaluated at `x`.
"""
function eval_g end

"""
   eval_jac_g(
      x::Vector{Float64},
      rows::Vector{Cint},
      cols::Vector{Cint},
      values::Union{Nothing,Vector{Float64}},
   )::Nothing

Compute the Jacobian matrix.

* If `values === nothing`
   - Fill `rows` and `cols` with the 1-indexed sparsity structure
* Otherwise:
   - Fill `values` with the elements of the Jacobian matrix according to the
     sparsity structure.

!!! warning
    If `values === nothing`, `x` is an undefined object. Accessing any elements
    in it will cause Julia to segfault.
"""
function eval_jac_g end

"""
   eval_h(
      x::Vector{Float64},
      rows::Vector{Cint},
      cols::Vector{Cint},
      obj_factor::Float64,
      lambda::Float64,
      values::Union{Nothing,Vector{Float64}},
   )::Nothing

Compute the Hessian-of-the-Lagrangian matrix.

* If `values === nothing`
   - Fill `rows` and `cols` with the 1-indexed sparsity structure
* Otherwise:
   - Fill `values` with the Hessian matrix according to the sparsity structure.

!!! warning
    If `values === nothing`, `x` is an undefined object. Accessing any elements
    in it will cause Julia to segfault.
"""
function eval_h end

If you get a termination status MOI.INVALID_MODEL, it is probably because you have some undefined value in your model, for example, a division by zero. Fix this by removing the division, or by imposing variable bounds so that you cut off the undefined region.

Instead of

model = Model(Ipopt.Optimizer)
@variable(model, x)
@NLobjective(model, 1 / x)

do

model = Model(Ipopt.Optimizer)
@variable(model, x >= 0.0001)
@NLobjective(model, 1 / x)

To improve performance, Ipopt supports a number of linear solvers.

Obtain a license and download HSL_jll.jl from https://licences.stfc.ac.uk/product/julia-hsl.

There are two versions available: LBT and OpenBLAS. LBT is the recommended option for Julia ≥ v1.9.

Install this download into your current environment using:

import Pkg
Pkg.develop(path = "/full/path/to/HSL_jll.jl")

Then, use a linear solver in HSL by setting the hsllib and linear_solver attributes:

using JuMP, Ipopt
import HSL_jll
model = Model(Ipopt.Optimizer)
set_attribute(model, "hsllib", HSL_jll.libhsl_path)
set_attribute(model, "linear_solver", "ma86")

Due to the security policy of macOS, Mac users may need to delete the quarantine attribute of the ZIP archive before extracting. For example:

xattr -d com.apple.quarantine lbt_HSL_jll.jl-2023.5.26.zip
xattr -d com.apple.quarantine openblas_HSL_jll.jl-2023.5.26.zip

Download Pardiso from https://www.pardiso-project.org. Save the shared library somewhere, and record the filename.

Then, use Pardiso by setting the pardisolib and linear_solver attributes:

using JuMP, Ipopt
model = Model(Ipopt.Optimizer)
set_attribute(model, "pardisolib", "/full/path/to/libpardiso")
set_attribute(model, "linear_solver", "pardiso")

If you use Ipopt.jl with Julia ≥ v1.9, the linear solver SPRAL is available. You can use it by setting the linear_solver attribute:

using JuMP, Ipopt
model = Model(Ipopt.Optimizer)
set_attribute(model, "linear_solver", "spral")

Note that the following environment variables must be set before starting Julia:

export OMP_CANCELLATION=TRUE
export OMP_PROC_BIND=TRUE

With Julia v1.9 or later, Ipopt and the linear solvers MUMPS (default), SPRAL, and HSL are compiled with libblastrampoline (LBT), a library that can change between BLAS and LAPACK backends at runtime.

The default BLAS and LAPACK backend is OpenBLAS.

Using LBT, we can also switch dynamically to other BLAS backends such as Intel MKL and Apple Accelerate. Because Ipopt and the linear solvers heavily rely on BLAS and LAPACK routines, using an optimized backend for a particular platform can improve the performance.

If you have MKL.jl installed, switch to MKL by adding using MKL to your code:

using MKL  # Replace OpenBLAS by Intel MKL
using Ipopt

If you are using macOS ≥ v13.4 and you have AppleAccelerate.jl installed, add using AppleAccelerate to your code:

using AppleAccelerate  # Replace OpenBLAS by Apple Accelerate
using Ipopt

Check what backends are loaded using:

import LinearAlgebra
LinearAlgebra.BLAS.lbt_get_config()