NLsolve.jl

This is a extension for importing solvers from NLsolve.jl into the SciML interface. Note that these solvers do not come by default, and thus one needs to install the package before using these solvers:

using Pkg
Pkg.add("NLsolve")
using NLSolve, NonlinearSolve

Solver API

NonlinearSolve.NLsolveJL — Type
NLsolveJL(; method = :trust_region, autodiff = :central, linesearch = Static(),
    linsolve = (x, A, b) -> copyto!(x, A\b), factor = one(Float64), autoscale = true,
    m = 10, beta = one(Float64))

Keyword Arguments

  • method: the choice of method for solving the nonlinear system.
  • autodiff: the choice of method for generating the Jacobian. Defaults to :central or central differencing via FiniteDiff.jl. The other choices are :forward or ADTypes similar to other solvers in NonlinearSolve.
  • linesearch: the line search method to be used within the solver method. The choices are line search types from LineSearches.jl.
  • linsolve: a function linsolve(x, A, b) that solves Ax = b.
  • factor: determines the size of the initial trust region. This size is set to the product of factor and the euclidean norm of u0 if nonzero, or else to factor itself.
  • autoscale: if true, then the variables will be automatically rescaled. The scaling factors are the norms of the Jacobian columns.
  • m: the amount of history in the Anderson method. Naive "Picard"-style iteration can be achieved by setting m=0, but that isn't advisable for contractions whose Lipschitz constants are close to 1. If convergence fails, though, you may consider lowering it.
  • beta: It is also known as DIIS or Pulay mixing, this method is based on the acceleration of the fixed-point iteration xₙ₊₁ = xₙ + beta*f(xₙ), where by default beta = 1.

Submethod Choice

Choices for methods in NLsolveJL:

  • :anderson: Anderson-accelerated fixed-point iteration
  • :broyden: Broyden's quasi-Newton method
  • :newton: Classical Newton method with an optional line search
  • :trust_region: Trust region Newton method (the default choice)

For more information on these arguments, consult the NLsolve.jl documentation.

Note

This algorithm is only available if NLsolve.jl is installed.