How to make MonteCarloMeasurements work with Optim

[hzgzh]

using MonteCarloMeasurements,Optim
f(x)=(1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2
x=[0.0±0.0,0.0±0.1]
optimize(f,x)

ERROR: MethodError: no method matching -(::Particles{Float64,2000}, ::Array{Float64,1}) Closest candidates are: -(::Particles{T,N}) where {T, N} at C:\Users\Administrator.julia\packages\MonteCarloMeasurements\J2g8U\src\register_primitive.jl:95 -(::Real, ::Complex{Bool}) at complex.jl:304 -(::Real, ::Complex) at complex.jl:316 ... Stacktrace: [1] (::Statistics.var"#8#9"{Array{Float64,1}})(::Particles{Float64,2000}) at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:219 [2] _mapreduce(::Statistics.var"#8#9"{Array{Float64,1}}, ::typeof(+), ::IndexLinear, ::Array{Particles{Float64,2000},1}) at .\reduce.jl:400 [3] _mapreduce_dim(::Function, ::Function, ::NamedTuple{(),Tuple{}}, ::Array{Particles{Float64,2000},1}, ::Colon) at .\reducedim.jl:312 [4] #mapreduce#580 at .\reducedim.jl:307 [inlined] [5] mapreduce(::Function, ::Function, ::Array{Particles{Float64,2000},1}) at .\reducedim.jl:307 [6] centralize_sumabs2(::Array{Particles{Float64,2000},1}, ::Array{Float64,1}) at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:220 [7] _varm(::Array{Particles{Float64,2000},1}, ::Array{Float64,1}, ::Bool, ::Colon) at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:307 [8] #varm#11 at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:297 [inlined] [9] _var at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:340 [inlined] [10] #var#15 at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:335 [inlined] [11] var at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\Statistics\src\Statistics.jl:335 [inlined] [12] nmobjective(::Array{Particles{Float64,2000},1}, ::Int64, ::Int64) at C:\Users\Administrator.julia\packages\Optim\SFpsz\src\multivariate\solvers\zeroth_order\nelder_mead.jl:104 [13] initial_state(::NelderMead{Optim.AffineSimplexer,Optim.AdaptiveParameters}, ::Optim.Options{Float64,Nothing}, ::NonDifferentiable{Particles{Float64,2000},Array{Particles{Float64,2000},1}}, ::Array{Particles{Float64,2000},1}) at C:\Users\Administrator.julia\packages\Optim\SFpsz\src\multivariate\solvers\zeroth_order\nelder_mead.jl:171 [14] optimize(::NonDifferentiable{Particles{Float64,2000},Array{Particles{Float64,2000},1}}, ::Array{Particles{Float64,2000},1}, ::NelderMead{Optim.AffineSimplexer,Optim.AdaptiveParameters}, ::Optim.Options{Float64,Nothing}) at C:\Users\Administrator.julia\packages\Optim\SFpsz\src\multivariate\optimize\optimize.jl:33 [15] optimize(::Function, ::Array{Particles{Float64,2000},1}; inplace::Bool, autodiff::Symbol, kwargs::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}) at C:\Users\Administrator.julia\packages\Optim\SFpsz\src\multivariate\optimize\interface.jl:64 [16] optimize(::Function, ::Array{Particles{Float64,2000},1}) at C:\Users\Administrator.julia\packages\Optim\SFpsz\src\multivariate\optimize\interface.jl:58

[18] eval(::Module, ::Any) at .\boot.jl:331 [19] eval_user_input(::Any, ::REPL.REPLBackend) at D:\buildbot\worker\package_win64\build\usr\share\julia\stdlib\v1.4\REPL\src\REPL.jl:86 [20] run_backend(::REPL.REPLBackend) at C:\Users\Administrator.julia\packages\Revise\tV8FE\src\Revise.jl:1165 [21] top-level scope at none:0

[baggepinnen]

See some of the examples https://github.com/baggepinnen/MonteCarloMeasurements.jl/blob/master/examples/autodiff_robust_opt.jl

https://github.com/baggepinnen/MonteCarloMeasurements.jl/blob/master/examples/robust_controller_opt.jl

[baggepinnen]

I think the problem is that your objective function is not a scalar, it's a distribution. I'm not sure if it makes sense to have the decision variable be uncertain, it makes more sense if the parameters of the cost function are uncertain. Here's an example where the problem parameters are uncertain and where the objective is reduced to a scalar

Example:

julia> const p1, p2 = 1 ∓ 0.3, 100 ∓ 5
(1.0 ± 0.3, 100.0 ± 5.0)

julia> f(x) = maximum((p1 - x[1])^2 + p2 * (x[2] - x[1]^2)^2)
f (generic function with 1 method)

julia> x = [0.5, 0.5]
2-element Array
{Float64,1}:
 0.5
 0.5

julia> res = optimize(f, x);

julia> @show res.minimizer
res.minimizer = [0.9999999905310097, 0.9999984765966677]
2-element Array{Float64,1}:
 0.9999999905310097
 0.9999984765966677

[hzgzh]

learn lot，need optim to support