Ipopt.jl

Ipopt.jl is a Julia interface to the COIN-OR nonlinear solver Ipopt.

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

Installation

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.

For details on using a different linear solver, see the Linear Solvers section below.

JuMP and MathOptInterface

You can use Ipopt with JuMP as follows:

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

Supported options are listed in the Ipopt documentation.

Solver-specific callback

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.

C Interface Wrapper

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

INVALID_MODEL error

If you get a termination status MOI.INVALID_MODEL, it is probably because you have some undefined value in your model, e.g., 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)

Linear Solvers

To improve performance, Ipopt supports a number of linear solvers. Installing these can be tricky, however, the following instructions should work. If they don't, or are not explicit enough, please open an issue.

Julia 1.7

Depending on your system, you may encounter the error: Error: no BLAS/LAPACK library loaded!. If you do, run:

import LinearAlgebra, OpenBLAS32_jll
LinearAlgebra.BLAS.lbt_forward(OpenBLAS32_jll.libopenblas_path)

Pardiso (Pardiso Project)

Linux

Tested on a clean install of Ubuntu 20.04.

1. Install lapack and libomp:

   sudo apt install liblapack3 libomp-dev
   

2. Download Pardiso from https://www.pardiso-project.org
3. Rename the file libpardiso-XXXXX.so to libpardiso.so
4. Place the libpardiso.so library somewhere on your load path

   • Alternatively, if the library is located at /full/path/libpardiso.so, start Julia with export LD_LIBRARY_PATH=/full/path; julia

     To make this permanent, modify your .bashrc to include:

     export LD_LIBRARY_PATH="${LD_LIBRARY_PATH}:/full/path/"
     

5. Set the option linear_solver to pardiso:

   using Libdl
   # Note: these filenames may differ. Check `/usr/lib/x86_64-linux-gnu` for the
   # specific extension.
   Libdl.dlopen("/usr/lib/x86_64-linux-gnu/liblapack.so.3", RTLD_GLOBAL)
   Libdl.dlopen("/usr/lib/x86_64-linux-gnu/libomp.so.5", RTLD_GLOBAL)
   
   using JuMP, Ipopt
   model = Model(Ipopt.Optimizer)
   set_optimizer_attribute(model, "linear_solver", "pardiso")

Mac

Tested on a MacBook Pro, 10.15.7.

1. Download Pardiso from https://www.pardiso-project.org
2. Rename the file libpardiso-XXXXX.dylib to libpardiso.dylib.
3. Place the libpardiso.dylib library somewhere on your load path.
   • Alternatively, if the library is located at /full/path/libpardiso.dylib, start Julia with export DL_LOAD_PATH=/full/path; julia
4. Set the option linear_solver to pardiso:

   using JuMP, Ipopt
   model = Model(Ipopt.Optimizer)
   set_optimizer_attribute(model, "linear_solver", "pardiso")

Windows

Currently untested. If you have instructions that work, please open an issue.

HSL (MA27, MA86, MA97)

Linux

Tested on a clean install of Ubuntu 20.04.

1. Install dependencies if necessary:

   sudo apt install gfortran libblas-dev libmetis-dev
   

   Note: on Windows Subsystem for Linux, you may also need sudo apt install make.
2. Download the appropriate version of HSL.
   • MA27: HSL for IPOPT from HSL
   • MA86: HSL_MA86 from HSL
   • Other: http://www.hsl.rl.ac.uk/catalogue/
3. Unzip the download, cd to the directory, and run the following:

   ./configure --prefix=</full/path/somewhere>
   make
   make install
   

   where </full/path/somewhere> is replaced as appropriate.
4. Rename the resutling HSL library to /full/path/somewhere/lib/libhsl.so.
   • For ma27, the file is /full/path/somewhere/lib/libcoinhsl.so
   • For ma86, the file is /full/path/somewhere/lib/libhsl_ma86.so
5. Place the libhsl.so library somewhere on your load path.
   • Alternatively, start Julia with export LD_LIBRARY_PATH=/full/path/somewhere/lib; julia
6. Set the option linear_solver to ma27 or ma86 as appropriate:

   using JuMP, Ipopt
   model = Model(Ipopt.Optimizer)
   set_optimizer_attribute(model, "linear_solver", "ma27")
   # or
   set_optimizer_attribute(model, "linear_solver", "ma86")

Mac

Tested on a MacBook Pro, 10.15.7.

1. Download the appropriate version of HSL.
   • MA27: HSL for IPOPT from HSL
   • MA86: HSL_MA86 from HSL
   • Other: http://www.hsl.rl.ac.uk/catalogue/
2. Unzip the download, cd to the directory, and run the following:

   ./configure --prefix=</full/path/somewhere>
   make
   make install
   

   where </full/path/somewhere> is replaced as appropriate.
3. Rename the resutling HSL library to /full/path/somewhere/lib/libhsl.dylib.
   • For ma27, the file is /full/path/somewhere/lib/libcoinhsl.dylib
   • For ma86, the file is /full/path/somewhere/lib/libhsl_ma86.dylib
4. Place the libhsl.dylib library somewhere on your load path.
   • Alternatively, start Julia with export DL_LOAD_PATH=/full/path/somewhere/lib; julia
5. Set the option linear_solver to ma27 or ma86 as appropriate:

   using JuMP, Ipopt
   model = Model(Ipopt.Optimizer)
   set_optimizer_attribute(model, "linear_solver", "ma27")
   # or
   set_optimizer_attribute(model, "linear_solver", "ma86")

Windows

Currently untested. If you have instructions that work, please open an issue.

Pardiso (MKL)

Currently untested on all platforms. If you have instructions that work, please open an issue.