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.
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_optimizer_attribute(model, "max_cpu_time", 60.0)
set_optimizer_attribute(model, "print_level", 0)
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.
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, 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)
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.
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)
Tested on a clean install of Ubuntu 20.04.
- Install lapack and libomp:
sudo apt install liblapack3 libomp-dev
- Download Pardiso from https://www.pardiso-project.org
- Rename the file
libpardiso-XXXXX.so
tolibpardiso.so
- Place the
libpardiso.so
library somewhere on your load path-
Alternatively, if the library is located at
/full/path/libpardiso.so
, start Julia withexport LD_LIBRARY_PATH=/full/path; julia
To make this permanent, modify your
.bashrc
to include:export LD_LIBRARY_PATH="${LD_LIBRARY_PATH}:/full/path/"
-
- Set the option
linear_solver
topardiso
: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")
Tested on a MacBook Pro, 10.15.7.
- Download Pardiso from https://www.pardiso-project.org
- Rename the file
libpardiso-XXXXX.dylib
tolibpardiso.dylib
. - Place the
libpardiso.dylib
library somewhere on your load path.- Alternatively, if the library is located at
/full/path/libpardiso.dylib
, start Julia withexport DL_LOAD_PATH=/full/path; julia
- Alternatively, if the library is located at
- Set the option
linear_solver
topardiso
:using JuMP, Ipopt model = Model(Ipopt.Optimizer) set_optimizer_attribute(model, "linear_solver", "pardiso")
Currently untested. If you have instructions that work, please open an issue.
Tested on a clean install of Ubuntu 20.04 and WSL Ubuntu 20.04
- Install dependencies if necessary:
Note: on Windows Subsystem for Linux, you may also need
sudo apt install gfortran libblas-dev libmetis-dev
sudo apt install make
. - Download the appropriate version of HSL.
- MA27: HSL for IPOPT from HSL
- MA86: HSL_MA86 from HSL
- Other: https://www.hsl.rl.ac.uk/catalogue/
- Unzip the download,
cd
to the directory, and run the following:where./configure --prefix=</full/path/somewhere> make make install
</full/path/somewhere>
is replaced as appropriate. - 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
- For
- Place the
libhsl.so
library somewhere on your load path.- Alternatively, start Julia with
export LD_LIBRARY_PATH=/full/path/somewhere/lib; julia
- Alternatively, start Julia with
- Set the option
linear_solver
toma27
orma86
as appropriate:using JuMP, Ipopt model = Model(Ipopt.Optimizer) set_optimizer_attribute(model, "linear_solver", "ma27") # or set_optimizer_attribute(model, "linear_solver", "ma86")
Tested on a MacBook Pro, 10.15.7, 12.6, 13.0
-
Download the appropriate version of HSL.
- MA27: HSL for IPOPT from HSL
- MA86: HSL_MA86 from HSL
- Other: https://www.hsl.rl.ac.uk/catalogue/
-
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. -
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
- For
-
Now we need to ensure Ipopt can find
libhsl.dylib
this can be achieved by either- Setting an environment variable
export DL_LOAD_PATH=/full/path/somewhere/lib
- Setting
hsllib
withset_optimizer_attribute(model, "hsllib","full/path/somewhere/lib/libhsl.dylib")
- Setting an environment variable
-
Set the option
linear_solver
toma27
orma86
as appropriate:using JuMP, Ipopt model = Model(Ipopt.Optimizer) set_optimizer_attribute(model, "linear_solver", "ma27") # or set_optimizer_attribute(model, "linear_solver", "ma86")
Currently untested. If you have instructions that work, please open an issue. Alternatively you can use Windows Subsystem for Linux and follow the linux instructions.
Currently untested on all platforms. If you have instructions that work, please open an issue.