Basic Functions

optimize(
    fdf, x₀;
    method,
    kw...
)

Find an optimizer for fdf, starting with the initial approximation x₀. method keyword chooses a specific optimization method. See optimize! for the description of other keywords.

optimize!(fdf, M::Wrapper, x0)

Find an optimizer for fdf, starting with the initial approximation x0. fdf(x, g) must return a tuple (f(x), ∇f(x)) and, if g is mutable, overwrite it with the gradient.

optimize!(
    fdf, M::OptBuffer, x₀;
    gtol=1e-6,
    convcond=nothing,
    maxiter=100,
    maxcalls=nothing,
    reset=true,
    constrain_step=nothing,
    tracking=nothing,
    verbosity=0
)

Find an optimizer for fdf, starting with the initial approximation x₀.

Arguments

• M::OptBuffer: the core method to use for optimization
• fdf(x, g)::Function: function to optimize. It must return a tuple (f(x), ∇f(x)) and, if g is mutable, overwrite it with the gradient.
• x0: initial approximation

Keywords

Convergence criteria

There are two options to specify convergence criterion. The default is by gtol and the second by custom stop convcond.

• gtol::Real: (default stop criterion) stop optimization when the gradient's 2-norm is less
• convcond=(x, xpre, y, ypre, g)->Bool: function, custom stop criterion based on argument values, function values and gradient. If nothing (default), corresponds to gtol, and when specified, the gtol-criterion is ignored.

Example (default criterion): convcond = (x, xpre, y, ypre, g) -> norm(g, 2) ≤ gtol.

Limitting optimization

(Un)Limit optimization process by specifing either maxiter and/or maxcalls.

• maxiter::Integer: force stop optimization after this number of iterations (use nothing or a negative value to not constrain iteration number)
• maxcalls::Integer: force stop optimization after this number of function calls (use nothing or a negative value to not constrain call number)

Optimization constrains

The inequality constrains of optimization is handled by constrain_step.

• constrain_step(x0, d): a function to constrain step from x0 in the direction d. It must return a real-numbered value α such that x0 + αd is the maximum allowed step

Initializing

• reset=true: a value to pass as a keyword argument to the optimizer init! method

Optimization path

• tracking::Union{Nothing,IO,AbstractString}: IO stream or a file name to log the optimization process or nothing to disable logging (default: nothing)
• verbosity::Integer: verbosity of logging. 0 (default) disables tracking. 1 logs all points of objective function evaluation with corresponding values and gradients. 2 shows additional statistics regarding the line search. Option ignored if tracking == nothing.

Downhill.solver(
    M::OptBuffer;
    gtol = 1e-6,
    maxiter = 100,
    maxcalls = nothing,
    constrain_step=nothing,
)

Return the wrapper object for a chosen method to solve an optimization problem with given parameters. For the description of keywords, see optimize!

Downhill.solver(
    M::DataType, x;
    gtol=1e-6, maxiter = 100, maxcalls = nothing, constrain_step)

Return the wrapper object for a chosen method to solve an optimization problem with given parameters compatible with the dimensions of x.