GitHub

Interior point method using Ipopt.jl

Description

Ipopt is a well known interior point optimizer developed and maintained by COIN-OR. The Julia wrapper of Ipopt is Ipopt.jl. Ipopt.jl is wrapped in NonconvexIpopt.jl. NonconvexIpopt allows the use of Ipopt.jl using the IpoptAlg algorithm struct. IpoptAlg can be used as a second order optimizer computing the Hessian of the Lagrangian in every iteration. Alternatively, an l-BFGS approximation of the Hessian can be used instead turning IpoptAlg into a first order optimizer tha only requires the gradient of the Lagrangian.

Quick start

Given a model model and an initial solution x0, the following can be used to optimize the model using Ipopt.

using Nonconvex
Nonconvex.@load Ipopt

alg = IpoptAlg()
options = IpoptOptions()
result = optimize(model, alg, x0, options = options)

Construct an instance

To construct an instance of the Ipopt algorithm, use:

alg = IpoptAlg()

Options

The options keyword argument to the optimize function shown above must be an instance of the IpoptOptions struct when the algorihm is an IpoptAlg. To specify options use keyword arguments in the constructor of IpoptOptions, e.g:

options = IpoptOptions(first_order = false, tol = 1e-4, sparse = false, symbolic = false)

There are 4 important and special options:

  • first_order: true by default. When first_order is true, the first order Ipopt algorithm will be used. And when it is false, the second order Ipopt algorithm will be used.
  • symbolic: false by default. When symbolic is set to true, the gradients, Jacobians and Hessians of the objective, constraint and Lagrangian functions will be calculated using symbolic differentiation from Symbolics.jl. This is the same approach used by symbolify which is described in the symbolic differentiation section in the documentation.
  • sparse: false by default. When sparse is set to true, the gradients, Jacobians and Hessians of the objective, constraint and Lagrangian functions will be treated as sparse vectors/matrices. When combined with symbolic = true, the output of symbolic differentiation will be a sparse vector/matrix, akin to setting sparse = true in the symbolify function discussed in symbolic differentiation section in the documentation. When used alone with symbolic = false, SparseDiffTools.jl is used instead for the differentiation and Symbolics is only used to get the sparsity pattern, much like how sparsify works. For more details on sparsify and the way SparseDiffTools works, see the sparsity section in the documentation is used instead.
  • linear_constraints: false by default. When linear_constraints is true, the Jacobian of the constraints will be computed and sparsified once at the beginning. When it is false, dense Jacobians will be computed in every iteration.

Note that there is no need to use sparsify or symbolify on the model or functions before optimizing it with an IpoptAlg. Setting the sparse and symbolic options above are enough to trigger the symbolic differentiation and/or sparsity exploitation.

All the other options that can be set can be found on the Ipopt options section of Ipopt's documentation.