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Configurable options

There are several options that simply take on some default values if the user doesn't supply anything else than a function (and gradient) and a starting point.

Solver options

There quite a few different solvers available in Optim, and they are all listed below. Notice that the constructors are written without input here, but they generally take keywords to tweak the way they work. See the pages describing each solver for more detail.

Requires only a function handle:

  • NelderMead()
  • SimulatedAnnealing()

Requires a function and gradient (will be approximated if omitted):

  • BFGS()
  • LBFGS()
  • ConjugateGradient()
  • GradientDescent()
  • MomentumGradientDescent()
  • AcceleratedGradientDescent()

Requires a function, a gradient, and a Hessian (cannot be omitted):

  • Newton()
  • NewtonTrustRegion()

Box constrained minimization:

  • Fminbox()

Special methods for bounded univariate optimization:

  • Brent()
  • GoldenSection()

General Options

In addition to the solver, you can alter the behavior of the Optim package by using the list of keyword below in the Optim.Options constructor.

Termination

  • x_abstol: Absolute tolerance in changes of the input vector x, in infinity norm. Defaults to 0.0.
  • x_reltol: Relative tolerance in changes of the input vector x, in infinity norm. Defaults to 0.0.
  • f_abstol: Absolute tolerance in changes of the objective value. Defaults to 0.0.
  • f_reltol: Relative tolerance in changes of the objective value. Defaults to 0.0.
  • g_abstol: Absolute tolerance in the gradient, in infinity norm. Defaults to 1e-8. For gradient free methods, this will control the main convergence tolerance, which is solver specific.
  • f_calls_limit: A soft upper limit on the number of objective calls. Defaults to 0 (unlimited).
  • g_calls_limit: A soft upper limit on the number of gradient calls. Defaults to 0 (unlimited).
  • h_calls_limit: A soft upper limit on the number of Hessian calls. Defaults to 0 (unlimited).
  • allow_f_increases: Allow steps that increase the objective value. Defaults to true. Note that, when this setting is true, the last iterate will be returned as the minimizer even if the objective increased.
  • successive_f_tol: Determines the number of times the objective is allowed to increase across iterations. Defaults to 1.
  • iterations: How many iterations will run before the algorithm gives up? Defaults to 1_000.
  • time_limit: A soft upper limit on the total run time. Defaults to NaN (unlimited).
  • callback: A function to be called during tracing. The return value should be a boolean, where true will stop the optimize call early. The callback function is called every show_everyth iteration. If store_trace is false, the argument to the callback is of the type OptimizationState, describing the state of the current iteration. If store_trace is true, the argument is a list of all the states from the first iteration to the current.

!!! tip "Disabling a termination criterion If the x_abstol, x_reltol, f_abstol, f_reltol, g_tol, or time_limit tolerances are set to NaN all comparisons will be false internally, and this fact can be used to turn off the check. For example, x_reltol defaults to 0. This does not mean that the check is turned off it only means that we stop at exactly zero change. However, if we set it to NaN specifically, the check of the termination criterion is always false and as such we will never stop due to any value of the infinity norm of the vector of relative changes.

Progress printing and storage

  • store_trace: Should a trace of the optimization algorithm's state be stored? Defaults to false.
  • show_trace: Should a trace of the optimization algorithm's state be shown on stdout? Defaults to false.
  • extended_trace: Save additional information. Solver dependent. Defaults to false.
  • trace_variables: A tuple of variable names given as Symbols to store in the trace. Defaults to (,), which means all variables are included.
  • show_warnings: Should warnings due to NaNs or Inf be shown? Defaults to true.
  • show_every: Trace output is printed every show_everyth iteration.
  • trace_simplex: Include the full simplex in the trace for NelderMead. Defaults to false.

Box constrained optimization (Fminbox)

Box constrained optimization has additional keywords to alter the behavior of the outer solver:

  • outer_x_abstol: Absolute tolerance in changes of the input vector x, in infinity norm. Defaults to 0.0.
  • outer_x_reltol: Relative tolerance in changes of the input vector x, in infinity norm. Defaults to 0.0.
  • outer_f_abstol: Absolute tolerance in changes of the objective value. Defaults to 0.0.
  • outer_f_reltol: Relative tolerance in changes of the objective value. Defaults to 0.0.
  • outer_g_tol: Absolute tolerance in the gradient, in infinity norm. Defaults to 1e-8. For gradient free methods, this will control the main convergence tolerance, which is solver specific.
  • allow_outer_f_increases: Allow steps that increase the objective value. Defaults to true. Note that, when this setting is true, the last iterate will be returned as the minimizer even if the objective increased.
  • outer_iterations: How many iterations will run before the algorithm gives up? Defaults to 1_000.

If you specify outer_iterations = 10 and iterations = 100, the outer algorithm will run for 10 iterations, and for each outer iteration the inner algorithm will run for 100 iterations.

Example usage

We currently recommend the statically dispatched interface by using the Optim.Options constructor:

res = optimize(f, g!,
               [0.0, 0.0],
               GradientDescent(),
               Optim.Options(g_tol = 1e-12,
                             iterations = 10,
                             store_trace = true,
                             show_trace = false,
                             show_warnings = true))

Another interface is also available, based directly on keywords:

res = optimize(f, g!,
               [0.0, 0.0],
               method = GradientDescent(),
               g_tol = 1e-12,
               iterations = 10,
               store_trace = true,
               show_trace = false,
               show_warnings = true)

Notice the need to specify the method using a keyword if this syntax is used. This approach might be deprecated in the future, and as a result we recommend writing code that has to maintained using the Optim.Options approach.