Add OncePerProcess versions

still segfault...
[skip ci]

Author: RomeoV

test/trim/main_once_per_process.jl

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+module MyModule
+include("./optimization_once_per_process.jl")
+end
+
+function (@main)(argv::Vector{String})::Cint
+    λ = parse(Float64, argv[1])
+    sol = MyModule.TestModuleTrimmable.minimize(λ)
+    println(Core.stdout, sum(sol.u))
+    return 0
+end

test/trim/optimization_once_per_process.jl

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+module TestModuleTrimmable
+using NonlinearSolveFirstOrder
+using DiffEqBase
+using ADTypes: AutoForwardDiff
+using ForwardDiff
+using LinearAlgebra
+using StaticArrays
+using LinearSolve
+import SciMLBase
+const LS = LinearSolve
+
+function f(u, p)
+    L, U = cholesky(p.Σ)
+    rhs = (u .* u .- p.λ)
+    # there are some issues currently with LinearSolve and triangular matrices,
+    # so we just make `L` dense here.
+    linprob = LinearProblem(Matrix(L), rhs)
+    alg = LS.GenericLUFactorization()
+    sol = LinearSolve.solve(linprob, alg)
+    return sol.u
+end
+
+struct MyParams{T, M}
+    λ::T
+    Σ::M
+end
+
+const cache = OncePerProcess() do
+    autodiff = AutoForwardDiff(; chunksize = 1)
+    alg = TrustRegion(; autodiff, linsolve = LS.CholeskyFactorization())
+    prob = NonlinearLeastSquaresProblem{false}(
+        f,
+        rand(2),
+        MyParams(rand(), hermitianpart(rand(2, 2) + 2I))
+    )
+    init(prob, alg)
+end
+
+function minimize(x)
+    ps = MyParams(x, hermitianpart(rand(2, 2) + 2I))
+    reinit!(cache(), rand(2); p = ps)
+    solve!(cache())
+    return cache
+end
+end