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First and second order mixed integer nonlinear programming algorithms

Description

There are 2 first and second order MINLP solvers available in Nonconvex:

  1. Juniper.jl with Ipopt.jl as a sub-solver. NonconvexJuniper.jl allows the use of the branch and bound algorithm in Juniper.jl using the JuniperIpoptAlg struct.
  2. Pavito.jl with Ipopt.jl and Cbc.jl as sub-solvers. NonconvexPavito.jl allows the use of the sequential polyhedral outer-approximations algorithm in Pavito.jl using the PavitoIpoptCbcAlg struct.

Juniper + Ipopt

Quick start

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

using Nonconvex
Nonconvex.@load Juniper

alg = JuniperIpoptAlg()
options = JuniperIpoptOptions()
result = optimize(model, alg, x0, options = options)

Juniper is an optional dependency of Nonconvex, so you need to load it in order to use it. Note that the integer constraints must be specified when defining variables. See the problem definition documentation for more details.

Construct an instance

To construct an instance of the Juniper + Ipopt algorithm, use:

alg = JuniperIpoptAlg()

Options

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

options = JuniperIpoptOptions(first_order = false, linear_constraints = true, subsolver_options = IpoptOptions(), atol = 1e-4)

There are 3 important and special options you can pass to the optimizer:

  • 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.
  • 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.
  • subsolver_options: an instance of IpoptOptions to be used in the Ipopt sub-solver.

All the other options to Juniper can be found in the Juniper documentation.

Pavito + Ipopt + Cbc

Quick start

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

using Nonconvex
Nonconvex.@load Pavito

alg = PavitoIpoptCbcAlg()
options = PavitoIpoptCbcOptions()
result = optimize(model, alg, x0, options = options)

Pavito is an optional dependency of Nonconvex, so you need to load it in order to use it. Note that the integer constraints must be specified when defining variables. See the problem definition documentation for more details.

Construct an instance

To construct an instance of the Pavito + Ipopt + Cbc algorithm, use:

alg = PavitoIpoptCbcAlg()

Options

The options keyword argument to the optimize function shown above must be an instance of PavitoIpoptCbcOptions struct when the algorithm is a PavitoIpoptCbcAlg. To specify options, use keyword arguments in the constructor of JuniperIpoptOptions or PavitoIpoptCbcOptions, e.g:

options = PavitoIpoptCbcOptions(first_order = false, subsolver_options = IpoptOptions(), timeout = 120.0)

There are 2 important and special options you can pass to the optimizer:

  • 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.
  • subsolver_options: an instance of IpoptOptions to be used in the Ipopt sub-solver.

All the other options to Pavito can be found in the Pavito documentation.