master.jl

julia> using Base.Test

julia> # Quadratic objective function
       # For (A*x-b)^2/2
       function quadratic!(x, g, AtA, Atb, tmp)
           calc_grad = !(g === nothing)
           A_mul_B!(tmp, AtA, x)
           v = dot(x,tmp)/2 + dot(Atb,x)
           if calc_grad
               for i = 1:length(g)
                   g[i] = tmp[i] + Atb[i]
               end
           end
           return v
       end
quadratic! (generic function with 1 method)

julia> srand(1)
MersenneTwister(Base.dSFMT.DSFMT_state(Int32[1749029653,1072851681,1610647787,1072862326,1841712345,1073426746,-198061126,1073322060,-156153802,1073567984  …  1977574422,1073209915,278919868,1072835605,1290372147,18858467,1815133874,-1716870370,382,-1]),[4.83826e-316,4.86122e-316,NaN,4.83592e-316,NaN,4.83597e-316,4.83847e-316,4.86128e-316,NaN,4.83592e-316  …  NaN,4.83585e-316,NaN,4.86131e-316,NaN,4.86125e-316,NaN,4.8358e-316,NaN,4.83578e-316],382,UInt32[0x00000001])

julia> N = 8
8

julia> boxl = 2.0
2.0

julia> outbox = false
false

julia> # Generate a problem where the bounds-free solution lies outside of the chosen box
       global objective

julia> while !outbox
           A = randn(N,N)
           AtA = A'*A
           b = randn(N)
           x0 = randn(N)
           tmp = similar(x0)
           func = (x, g) -> quadratic!(x, g, AtA, A'*b, tmp)
           objective = Optim.DifferentiableFunction(x->func(x, nothing), (x,g)->func(x,g), func)
           results = Optim.optimize(objective, x0, method=ConjugateGradient())
           results = Optim.optimize(objective, results.minimum, method=ConjugateGradient())  # restart to ensure high-precision convergence
           @test Optim.converged(results)
           g = similar(x0)
           @test func(results.minimum, g) + dot(b,b)/2 < 1e-8
           @test norm(g) < 1e-4
           outbox = any(abs(results.minimum) .> boxl)
       end

julia> # fminbox
       l = fill(-boxl, N)
8-element Array{Float64,1}:
 -2.0
 -2.0
 -2.0
 -2.0
 -2.0
 -2.0
 -2.0
 -2.0

julia> u = fill(boxl, N)
8-element Array{Float64,1}:
 2.0
 2.0
 2.0
 2.0
 2.0
 2.0
 2.0
 2.0

julia> x0 = (rand(N)-0.5)*boxl
8-element Array{Float64,1}:
  0.906414 
 -0.231177 
 -0.359978 
  0.73125  
 -0.0908605
 -0.159427 
 -0.549698 
 -0.427662 

julia> for _optimizer in (ConjugateGradient, GradientDescent, LBFGS, BFGS)
           results = Optim.optimize(objective, x0, l, u, Fminbox(), optimizer = _optimizer)
           @test Optim.converged(results)

           g = similar(x0)
           objective.fg!(Optim.minimizer(results), g)
           for i = 1:N
               @test abs(g[i]) < 3e-3 || (Optim.minimizer(results)[i] < -boxl+1e-3 && g[i] > 0) || (Optim.minimizer(results)[i] > boxl-1e-3 && g[i] < 0)
           end
       end
WARNING: could not attach metadata for @simd loop.

julia> # tests for #180
       results = Optim.optimize(objective, x0, l, u, Fminbox(); iterations = 2)
Results of Optimization Algorithm
 * Algorithm: Fminbox with Conjugate Gradient
 * Starting Point: [0.9064140813027981,-0.2311772762956541, ...]
 * Minimizer: [-0.5461411516178056,1.9998156114199215, ...]
 * Minimum: -3.468544e+00
 * Iterations: 2
 * Convergence: true
   * |x - x'| < 1.0e-32: false
   * |f(x) - f(x')| / |f(x)| < 1.0e-08: true
   * |g(x)| < 1.0e-08: false
   * Reached Maximum Number of Iterations: false
 * Objective Function Calls: 237
 * Gradient Calls: 168

julia> @test results.iterations == 2

julia> @test results.f_minimum == objective.f(results.minimum)

julia> # might fail if changes are made to Optim.jl
       # TODO: come up with a better test
       results = Optim.optimize(objective, x0, l, u, Fminbox(); optimizer_o = OptimizationOptions(iterations = 2))
Results of Optimization Algorithm
 * Algorithm: Fminbox with Conjugate Gradient
 * Starting Point: [0.9064140813027981,-0.2311772762956541, ...]
 * Minimizer: [-0.5469850993943096,1.9999999999999998, ...]
 * Minimum: -3.468380e+00
 * Iterations: 470
 * Convergence: true
   * |x - x'| < 1.0e-32: false
   * |f(x) - f(x')| / |f(x)| < 1.0e-08: true
   * |g(x)| < 1.0e-08: false
   * Reached Maximum Number of Iterations: false
 * Objective Function Calls: 3894
 * Gradient Calls: 2942

julia> @test results.iterations == 470

julia>