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Prepare for ConstrainedProblems (#9)
* Add ConstrainedProblems module * Create MultivariateProblems module * Add the Beale unconstrained problem
1 parent 3024c55 commit a0d0464

8 files changed

+294
-84
lines changed

‎src/OptimTestProblems.jl

+7-1
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,12 @@
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module OptimTestProblems
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3-
include("optim_tests/multivariate/unconstrained.jl")
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export MultivariateProblems, UnivariateProblems
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include("optim_tests/multivariate/multivariate.jl")
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include("optim_tests/univariate/bounded.jl")
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# Deprecation stuff
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UnconstrainedProblems = OptimTestProblems.MultivariateProblems.UnconstrainedProblems
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export UnconstrainedProblems
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end # module

‎src/optim_tests/multivariate/constrained.jl

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@@ -0,0 +1,46 @@
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module ConstrainedProblems
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using ..OptimizationProblem,..ConstraintData
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examples = Dict{AbstractString, OptimizationProblem}()
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hs9_obj(x::AbstractVector) = sin(π*x[1]/12) * cos(π*x[2]/16)
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hs9_c!(c::AbstractVector, x::AbstractVector) = (c[1] = 4*x[1]-3*x[2]; c)
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hs9_h!(h, x, λ) = h
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function hs9_obj_g!(g::AbstractVector, x::AbstractVector)
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g[1] = π/12 * cos(π*x[1]/12) * cos(π*x[2]/16)
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g[2] = -π/16 * sin(π*x[1]/12) * sin(π*x[2]/16)
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g
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end
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function hs9_obj_h!(h::AbstractMatrix, x::AbstractVector)
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v = hs9_obj(x)
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h[1,1] = -π^2*v/144
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h[2,2] = -π^2*v/256
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h[1,2] = h[2,1] = -π^2 * cos(π*x[1]/12) * sin(π*x[2]/16) / 192
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h
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end
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function hs9_jacobian!(J, x)
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J[1,1] = 4
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J[1,2] = -3
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J
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end
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# TODO: IPNewtons gets stuck when using x0 = [0,0].
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# Check with Tim if this also happened before?
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examples["HS9"] = OptimizationProblem("HS9",
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hs9_obj,
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hs9_obj_g!,
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nothing,
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hs9_obj_h!,
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ConstraintData(hs9_c!, hs9_jacobian!, hs9_h!,
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[], [], [0.0], [0.0]),
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[-1.0,2.0],#[0.0, 0.0],
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[-3.0,-4.0],#[[12k-3, 16k-4] for k in (0, 1, -1)], # any integer k will do...
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hs9_obj([-3.0,-4.0]),
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true,
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true)
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end # module

‎src/optim_tests/multivariate/from_optim.jl

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@@ -31,8 +31,9 @@ end
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examples["Exponential"] = OptimizationProblem("Exponential",
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exponential,
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exponential_gradient!,
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nothing,
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nothing, # fg!
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exponential_hessian!,
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nothing, # Constraints
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[0.0, 0.0],
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[2.0, 3.0],
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exponential([2.0, 3.0]),
@@ -122,6 +123,7 @@ examples["Fletcher-Powell"] = OptimizationProblem("Fletcher-Powell",
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fletcher_powell_gradient!,
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fletcher_powell_fun_gradient!,
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fletcher_powell_hessian!,
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nothing, # Constraints
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[-1.0, 0.0, 0.0], # Same as in source
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[1.0, 0.0, 0.0],
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0.0,
@@ -157,6 +159,7 @@ examples["Himmelblau"] = OptimizationProblem("Himmelblau",
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himmelblau_gradient!,
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nothing,
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himmelblau_hessian!,
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nothing, # Constraints
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[2.0, 2.0],
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[3.0, 2.0],
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himmelblau([3.0, 2.0]),
@@ -191,6 +194,7 @@ examples["Hosaki"] = OptimizationProblem("Hosaki",
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hosaki_gradient!,
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nothing,
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hosaki_hessian!,
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nothing, # Constraints
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[3.6, 1.9],
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[4.0, 2.0],
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hosaki([4.0, 2.0]),
@@ -235,6 +239,7 @@ examples["Large Polynomial"] = OptimizationProblem("Large Polynomial",
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large_polynomial_gradient!,
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nothing,
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large_polynomial_hessian!,
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nothing, # Constraints
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zeros(250),
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collect(float(1:250)),
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large_polynomial(collect(float(1:250))),
@@ -277,6 +282,7 @@ examples["Parabola"] = OptimizationProblem("Parabola",
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parabola_gradient!,
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nothing,
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parabola_hessian!,
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nothing, # Constraints
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[0.0, 0.0, 0.0, 0.0, 0.0],
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[1.0, 2.0, 3.0, 5.0, 8.0],
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parabola([1.0, 2.0, 3.0, 5.0, 8.0]),
@@ -316,6 +322,7 @@ examples["Polynomial"] = OptimizationProblem("Polynomial",
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polynomial_gradient!,
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nothing,
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polynomial_hessian!,
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nothing, # Constraints
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[0.0, 0.0, 0.0],
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[10.0, 7.0, 108.0],
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polynomial([10.0, 7.0, 108.0]),
@@ -366,6 +373,7 @@ examples["Powell"] = OptimizationProblem("Powell",
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powell_gradient!,
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nothing,
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powell_hessian!,
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nothing, # Constraints
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[3.0, -1.0, 0.0, 1.0],
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[0.0, 0.0, 0.0, 0.0],
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powell([0.0, 0.0, 0.0, 0.0]),
@@ -402,6 +410,7 @@ examples["Rosenbrock"] = OptimizationProblem("Rosenbrock",
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rosenbrock_gradient!,
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nothing,
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rosenbrock_hessian!,
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nothing, # Constraints
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[-1.2, 1.0],
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[1.0, 1.0],
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rosenbrock([1.0, 1.0]),

‎src/optim_tests/multivariate/more_testing.jl

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@@ -63,6 +63,7 @@ function _extrosenbrockproblem(N::Int;
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extrosenbrock_gradient!,
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extrosenbrock_fun_gradient!,
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extrosenbrock_hessian!,
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nothing, # Constraints
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initial_x,
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ones(initial_x),
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zero(T),
@@ -155,6 +156,7 @@ function _extpowellproblem(N::Int;
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extpowell_gradient!,
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extpowell_fun_gradient!,
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extpowell_hessian!,
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nothing, # Constraints
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initial_x,
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zeros(initial_x),
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zero(T),
@@ -194,7 +196,7 @@ function penfunI_gradient!(storage::AbstractArray,
194196
end
195197

196198
function penfunI_fun_gradient!(storage::AbstractArray,
197-
x::AbstractArray, param)
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x::AbstractArray, param)
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# TODO: we could do this without the xt storage holder
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xt = param.xt
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@. xt = param.alpha*(x-one(eltype(x)))
@@ -231,6 +233,7 @@ function _penfunIproblem(N::Int;
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penfunI_gradient!,
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penfunI_fun_gradient!,
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penfunI_hessian!,
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nothing, # Constraints
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initial_x,
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xsol,
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fsol,
@@ -273,7 +276,7 @@ function trigonometric_gradient!(storage::AbstractArray,
273276
end
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275278
function trigonometric_fun_gradient!(storage::AbstractArray,
276-
x::AbstractArray, param)
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x::AbstractArray, param)
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# TODO: we could do this without the xt storage holder
278281
n = length(x)
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xt = param.vec
@@ -298,6 +301,7 @@ function _trigonometricproblem(N::Int;
298301
trigonometric_gradient!,
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trigonometric_fun_gradient!,
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trigonometric_hessian!,
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nothing, # Constraints
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initial_x,
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zeros(initial_x),
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zero(T),
@@ -307,3 +311,70 @@ function _trigonometricproblem(N::Int;
307311
end
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309313
examples["Trigonometric"] = _trigonometricproblem(100)
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##########################################################################
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###
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### Beale (2D)
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###
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### Problem 5 in [3]
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###
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### Sum-of-squares objective, non-convex with g'*inv(H)*g == 0 at the
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### initial position.
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###
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##########################################################################
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### General utilities for sum-of-squares functions
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# TODO: Update the other problems that are not Beale to use sumsq as well?
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# Requires f(x) and J(x) computes the values and jacobian at x of a set of functions, and
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# that H(x, i) computes the hessian of the ith function
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sumsq_obj(f, x) = sum(f(x).^2)
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function sumsq_gradient!(g::AbstractVector, f, J, x::AbstractVector)
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copy!(g, sum((2.0 .* f(x)) .* J(x), 1))
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end
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function sumsq_hessian!(h::AbstractMatrix, f, J, H, x::AbstractVector)
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fx = f(x)
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Jx = J(x)
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htmp = 2.0 .* (Jx' * Jx)
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for i = 1:length(fx)
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htmp += (2.0 * fx[i]) * H(x, i)
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end
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copy!(h, htmp)
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end
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const beale_y = [1.5, 2.25, 2.625]
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beale_f(x) = [beale_y[i] - x[1]*(1-x[2]^i) for i = 1:3]
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beale_J(x) = hcat([-(1-x[2]^i) for i = 1:3],
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[i*x[1]*x[2]^(i-1) for i = 1:3])
354+
function beale_H(x, i)
355+
od = i*x[2]^(i-1)
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d2 = i > 1 ? i*(i-1)*x[1]*x[2]^(i-2) : zero(x[2])
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[0 od; od d2]
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end
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beale(x::AbstractVector) = sumsq_obj(beale_f, x)
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function beale_gradient!(g::AbstractVector, x::AbstractVector)
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sumsq_gradient!(g, beale_f, beale_J, x)
364+
end
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366+
function beale_hessian!(h::AbstractMatrix, x::AbstractVector)
367+
sumsq_hessian!(h, beale_f, beale_J, beale_H, x)
368+
end
369+
370+
examples["Beale"] = OptimizationProblem("Beale",
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beale,
372+
beale_gradient!,
373+
nothing,
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beale_hessian!,
375+
nothing, # Constraints
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[1.0, 1.0],
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[3.0, 0.5],
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beale([3.0, 0.5]),
379+
true,
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true)

‎src/optim_tests/multivariate/multivariate.jl

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module MultivariateProblems
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import Base.gradient
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export UnconstrainedProblems
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export OptimizationProblem, objective, gradient, objective_gradient, hessian
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9+
struct ConstraintData{F,J,H,Tx,Tc}
10+
c!::F
11+
jacobian!::J
12+
h!::H
13+
lx::Vector{Tx}
14+
ux::Vector{Tx}
15+
lc::Vector{Tc}
16+
uc::Vector{Tc}
17+
end
18+
19+
immutable OptimizationProblem{P, Tfg, Tf <: Real, TS <: AbstractString,
20+
CT <: Union{Void,ConstraintData}}
21+
name::TS
22+
f::Function
23+
g!::Function
24+
fg!::Tfg
25+
h!::Function
26+
constraintdata::CT
27+
initial_x::Vector
28+
solutions::Vector
29+
minimum::Tf
30+
isdifferentiable::Bool
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istwicedifferentiable::Bool
32+
parameters::P
33+
end
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OptimizationProblem(name::AbstractString,
36+
f::Function,
37+
g!::Function,
38+
fg!::Tfg,
39+
h!::Function,
40+
constraints::Union{Void,ConstraintData},
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initial_x::Vector,
42+
solutions::Vector,
43+
minimum::Tf,
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isdifferentiable::Bool,
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istwicedifferentiable::Bool) where Tf where Tfg =
46+
OptimizationProblem(name, f, g!, fg!, h!, constraints,
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initial_x, solutions, minimum,
48+
isdifferentiable,
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istwicedifferentiable,
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nothing)
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objective(p::OptimizationProblem{P}) where P<:Void = p.f
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gradient(p::OptimizationProblem{P}) where P<:Void = p.g!
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objective_gradient(p::OptimizationProblem{P}) where P<:Void = p.fg!
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hessian(p::OptimizationProblem{P}) where P<:Void = p.h!
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57+
objective(p::OptimizationProblem{P}) where P = x-> p.f(x,p.parameters)
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gradient(p::OptimizationProblem{P}) where P = (out,x)-> p.g!(out,x,p.parameters)
59+
objective_gradient(p::OptimizationProblem{P}) where P = (out,x)-> p.fg!(out,x,p.parameters)
60+
hessian(p::OptimizationProblem{P}) where P = (out,x)-> p.h!(out,x,p.parameters)
61+
62+
function objective_gradient(p::OptimizationProblem{P,Tfg}) where P where Tfg <: Void
63+
(out,x) -> begin
64+
gradient(p)(out,x)
65+
return objective(p)(x)
66+
end
67+
end
68+
69+
function objective_gradient(p::OptimizationProblem{P,Tfg}) where P <: Void where Tfg <: Void
70+
(out,x) -> begin
71+
gradient(p)(out,x)
72+
return objective(p)(x)
73+
end
74+
end
75+
76+
77+
include("unconstrained.jl")
78+
include("constrained.jl")
79+
80+
end

‎src/optim_tests/multivariate/quad_transforms.jl

+2
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@@ -43,6 +43,7 @@ function _quadraticproblem(N::Int; mat::AbstractArray{T,2} = spdiagm(float(1:N))
4343
quad_gradient!,
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quad_fun_gradient!,
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quad_hessian!,
46+
nothing, # Constraints
4647
initial_x,
4748
x0,
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zero(T),
@@ -113,6 +114,7 @@ function _paraboloidproblem(N::Int; mat::AbstractArray{T,2} = spdiagm(float(1:N)
113114
paraboloid_gradient!,
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paraboloid_fun_gradient!,
115116
paraboloid_hessian!,
117+
nothing, # Constraints
116118
initial_x,
117119
x0, # x0 means the solution ...
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zero(T),

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