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Provide overoading point for arrays with custom axes #883

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This PR adds a function that can be overloaded for arrays with custom axes, so that these axes are preserved in the ParticleSwarmoptimization algorithm. The particular use case I have in mind is to formulate my objective function using ComponentArrays.jl, this works for most optimizers, but not for ParticleSwarm This PR introduces the function similar_axes that can be defined for custom arrays to do something sensible, e.g.,

julia> Optim.similar_axis(x::ComponentArray, n) = x .* zeros(length(x), n)

julia> a
ComponentVector{Float64}(a = [0.0, 0.0], b = [1.0, 1.0])

julia> f(x) = sum(abs2, x.a)+sum(abs, x.b)
f

julia> optimize(f, a, ParticleSwarm())
 * Status: failure (reached maximum number of iterations)

 * Candidate solution
    Final objective value:     5.214465e-84

 * Found with
    Algorithm:     Particle Swarm

 * Convergence measures
    |x - x'|               = NaN  0.0e+00
    |x - x'|/|x'|          = NaN  0.0e+00
    |f(x) - f(x')|         = NaN  0.0e+00
    |f(x) - f(x')|/|f(x')| = NaN  0.0e+00
    |g(x)|                 = NaN  1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    1000
    f(x) calls:    5001
    ∇f(x) calls:   0

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pkofod commented Nov 24, 2020

Thanks, I'll have a look. I'm inches from handing in my thesis though so it might be a few weeks. Please ping me if I forget :)

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pkofod commented Dec 16, 2020

This might be a good solution, but I'm thinking that actually these should just be vectors of copies of the input array? That's how I do it in the new version https://github.com/pkofod/NLSolvers.jl/blob/65034bb76cbf91e22784bd0156f28b85416adb2f/src/optimize/randomsearch/particleswarm.jl#L28

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