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nlp.jl
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nlp.jl
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using Base.Test
using MathProgBase
# Here the type represents the complete instance, but it
# could also store instance data.
type HS071 <: MathProgBase.AbstractNLPEvaluator
end
# hs071
# min x1 * x4 * (x1 + x2 + x3) + x3
# st x1 * x2 * x3 * x4 >= 25
# x1^2 + x2^2 + x3^2 + x4^2 = 40
# 1 <= x1, x2, x3, x4 <= 5
# Start at (1,5,5,1)
# End at (1.000..., 4.743..., 3.821..., 1.379...)
function MathProgBase.initialize(d::HS071, requested_features::Vector{Symbol})
for feat in requested_features
if !(feat in [:Grad, :Jac, :Hess])
error("Unsupported feature $feat")
# TODO: implement Jac-vec and Hess-vec products
# for solvers that need them
end
end
end
MathProgBase.features_available(d::HS071) = [:Grad, :Jac, :Hess]
MathProgBase.eval_f(d::HS071, x) = x[1] * x[4] * (x[1] + x[2] + x[3]) + x[3]
function MathProgBase.eval_g(d::HS071, g, x)
g[1] = x[1] * x[2] * x[3] * x[4]
g[2] = x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2
end
function MathProgBase.eval_grad_f(d::HS071, grad_f, x)
grad_f[1] = x[1] * x[4] + x[4] * (x[1] + x[2] + x[3])
grad_f[2] = x[1] * x[4]
grad_f[3] = x[1] * x[4] + 1
grad_f[4] = x[1] * (x[1] + x[2] + x[3])
end
MathProgBase.jac_structure(d::HS071) = [1,1,1,1,2,2,2,2],[1,2,3,4,1,2,3,4]
# lower triangle only
MathProgBase.hesslag_structure(d::HS071) = [1,2,2,3,3,3,4,4,4,4],[1,1,2,1,2,3,1,2,3,4]
function MathProgBase.eval_jac_g(d::HS071, J, x)
# Constraint (row) 1
J[1] = x[2]*x[3]*x[4] # 1,1
J[2] = x[1]*x[3]*x[4] # 1,2
J[3] = x[1]*x[2]*x[4] # 1,3
J[4] = x[1]*x[2]*x[3] # 1,4
# Constraint (row) 2
J[5] = 2*x[1] # 2,1
J[6] = 2*x[2] # 2,2
J[7] = 2*x[3] # 2,3
J[8] = 2*x[4] # 2,4
end
function MathProgBase.eval_hesslag(d::HS071, H, x, σ, μ)
# Again, only lower left triangle
# Objective
H[1] = σ * (2*x[4]) # 1,1
H[2] = σ * ( x[4]) # 2,1
H[3] = 0 # 2,2
H[4] = σ * ( x[4]) # 3,1
H[5] = 0 # 3,2
H[6] = 0 # 3,3
H[7] = σ* (2*x[1] + x[2] + x[3]) # 4,1
H[8] = σ * ( x[1]) # 4,2
H[9] = σ * ( x[1]) # 4,3
H[10] = 0 # 4,4
# First constraint
H[2] += μ[1] * (x[3] * x[4]) # 2,1
H[4] += μ[1] * (x[2] * x[4]) # 3,1
H[5] += μ[1] * (x[1] * x[4]) # 3,2
H[7] += μ[1] * (x[2] * x[3]) # 4,1
H[8] += μ[1] * (x[1] * x[3]) # 4,2
H[9] += μ[1] * (x[1] * x[2]) # 4,3
# Second constraint
H[1] += μ[2] * 2 # 1,1
H[3] += μ[2] * 2 # 2,2
H[6] += μ[2] * 2 # 3,3
H[10] += μ[2] * 2 # 4,4
end
function nlptest(solver=MathProgBase.defaultNLPsolver)
m = MathProgBase.model(solver)
l = [1,1,1,1]
u = [5,5,5,5]
lb = [25, 40]
ub = [Inf, 40]
MathProgBase.loadnonlinearproblem!(m, 4, 2, l, u, lb, ub, :Min, HS071())
MathProgBase.setwarmstart!(m,[1,5,5,1])
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
x = MathProgBase.getsolution(m)
@test_approx_eq_eps x[1] 1.0000000000000000 1e-5
@test_approx_eq_eps x[2] 4.7429996418092970 1e-5
@test_approx_eq_eps x[3] 3.8211499817883077 1e-5
@test_approx_eq_eps x[4] 1.3794082897556983 1e-5
@test_approx_eq_eps MathProgBase.getobjval(m) 17.014017145179164 1e-5
# Test that a second call to optimize! works
MathProgBase.setwarmstart!(m,[1,5,5,1])
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
end
# Same as above but no hessian callback
type HS071_2 <: MathProgBase.AbstractNLPEvaluator
end
# hs071
# min x1 * x4 * (x1 + x2 + x3) + x3
# st x1 * x2 * x3 * x4 >= 25
# x1^2 + x2^2 + x3^2 + x4^2 = 40
# 1 <= x1, x2, x3, x4 <= 5
# Start at (1,5,5,1)
# End at (1.000..., 4.743..., 3.821..., 1.379...)
function MathProgBase.initialize(d::HS071_2, requested_features::Vector{Symbol})
for feat in requested_features
if !(feat in [:Grad, :Jac])
error("Unsupported feature $feat")
# TODO: implement Jac-vec and Hess-vec products
# for solvers that need them
end
end
end
MathProgBase.features_available(d::HS071_2) = [:Grad, :Jac]
MathProgBase.eval_f(d::HS071_2, x) = MathProgBase.eval_f(HS071(), x)
MathProgBase.eval_g(d::HS071_2, g, x) = MathProgBase.eval_g(HS071(), g, x)
MathProgBase.eval_grad_f(d::HS071_2, grad_f, x) = MathProgBase.eval_grad_f(HS071(), grad_f, x)
MathProgBase.jac_structure(d::HS071_2) = MathProgBase.jac_structure(HS071())
MathProgBase.eval_jac_g(d::HS071_2, J, x) = MathProgBase.eval_jac_g(HS071(), J, x)
function nlptest_nohessian(solver=MathProgBase.defaultNLPsolver)
m = MathProgBase.model(solver)
l = [1,1,1,1]
u = [5,5,5,5]
lb = [25, 40]
ub = [Inf, 40]
MathProgBase.loadnonlinearproblem!(m, 4, 2, l, u, lb, ub, :Min, HS071_2())
MathProgBase.setwarmstart!(m,[1,5,5,1])
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
x = MathProgBase.getsolution(m)
@test_approx_eq_eps x[1] 1.0000000000000000 1e-5
@test_approx_eq_eps x[2] 4.7429996418092970 1e-5
@test_approx_eq_eps x[3] 3.8211499817883077 1e-5
@test_approx_eq_eps x[4] 1.3794082897556983 1e-5
@test_approx_eq_eps MathProgBase.getobjval(m) 17.014017145179164 1e-5
# Test that a second call to optimize! works
MathProgBase.setwarmstart!(m,[1,5,5,1])
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
end
# a test for convex nonlinear solvers
type QCQP <: MathProgBase.AbstractNLPEvaluator
end
# min x - y
# st x + x^2 + x*y + y^2 <= 1
# -2 <= x, y <= 2
# solution: x+y = -1/3
# optimal objective -1-4/sqrt(3)
function MathProgBase.initialize(d::QCQP, requested_features::Vector{Symbol})
for feat in requested_features
if !(feat in [:Grad, :Jac, :Hess])
error("Unsupported feature $feat")
# TODO: implement Jac-vec and Hess-vec products
# for solvers that need them
end
end
end
MathProgBase.features_available(d::QCQP) = [:Grad, :Jac, :Hess]
MathProgBase.eval_f(d::QCQP, x) = x[1]-x[2]
function MathProgBase.eval_g(d::QCQP, g, x)
g[1] = x[1] + x[1]^2 + x[1]*x[2] + x[2]^2
end
function MathProgBase.eval_grad_f(d::QCQP, grad_f, x)
grad_f[1] = 1
grad_f[2] = -1
end
MathProgBase.jac_structure(d::QCQP) = [1,1],[1,2]
# lower triangle only
MathProgBase.hesslag_structure(d::QCQP) = [1,2,2],[1,1,2]
function MathProgBase.eval_jac_g(d::QCQP, J, x)
J[1] = 1 + 2x[1] + x[2]
J[2] = x[1]+2x[2]
end
function MathProgBase.eval_hesslag(d::QCQP, H, x, σ, μ)
# Again, only lower left triangle
# Objective, linear
# First constraint
H[1] = 2μ[1] # d/dx^2
H[2] = μ[1] # d/dxdy
H[3] = 2μ[1] # d/dy^2
end
function convexnlptest(solver=MathProgBase.defaultNLPsolver)
m = MathProgBase.model(solver)
l = [-2,-2]
u = [2,2]
lb = [-Inf]
ub = [1.0]
MathProgBase.loadnonlinearproblem!(m, 2, 1, l, u, lb, ub, :Min, QCQP())
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
x = MathProgBase.getsolution(m)
@test_approx_eq_eps (x[1]+x[2]) -1/3 1e-3
@test_approx_eq_eps MathProgBase.getobjval(m) -1-4/sqrt(3) 1e-5
# Test that a second call to optimize! works
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
end
# a test for unconstrained nonlinear solvers
type Rosenbrock <: MathProgBase.AbstractNLPEvaluator
end
# min (1-x)^2 + 100*(y-x^2)^2
# solution: (x,y) = (1,1)
# optimal objective 0
function MathProgBase.initialize(d::Rosenbrock, requested_features::Vector{Symbol})
for feat in requested_features
if !(feat in [:Grad, :Jac, :Hess])
error("Unsupported feature $feat")
# TODO: implement Jac-vec and Hess-vec products
# for solvers that need them
end
end
end
MathProgBase.features_available(d::Rosenbrock) = [:Grad, :Jac, :Hess]
MathProgBase.eval_f(d::Rosenbrock, x) = (1-x[1])^2 + 100*(x[2]-x[1]^2)^2
MathProgBase.eval_g(d::Rosenbrock, g, x) = nothing
function MathProgBase.eval_grad_f(d::Rosenbrock, grad_f, x)
grad_f[1] = -2*(1-x[1]) - 400*x[1]*(x[2]-x[1]^2)
grad_f[2] = 200*(x[2]-x[1]^2)
end
MathProgBase.jac_structure(d::Rosenbrock) = Int[],Int[]
MathProgBase.hesslag_structure(d::Rosenbrock) = [1,2,2],[1,1,2]
MathProgBase.eval_jac_g(d::Rosenbrock, J, x) = nothing
function MathProgBase.eval_hesslag(d::Rosenbrock, H, x, σ, μ)
# Again, only lower left triangle
H[1] = σ*(2+100*(8x[1]^2-4*(x[2]-x[1]^2))) # d/dx^2
H[2] = -σ*400*x[1] # d/dxdy
H[3] = σ*200 # d/dy^2
end
function rosenbrocktest(solver=MathProgBase.defaultNLPsolver)
m = MathProgBase.model(solver)
l = [-Inf,-Inf]
u = [Inf,Inf]
lb = Float64[]
ub = Float64[]
MathProgBase.loadnonlinearproblem!(m, 2, 0, l, u, lb, ub, :Min, Rosenbrock())
MathProgBase.setwarmstart!(m,[10.0,10.0])
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
x = MathProgBase.getsolution(m)
@test_approx_eq_eps x[1] 1.0 1e-5
@test_approx_eq_eps x[2] 1.0 1e-5
@test_approx_eq_eps MathProgBase.getobjval(m) 0.0 1e-5
# Test that a second call to optimize! works
MathProgBase.optimize!(m)
stat = MathProgBase.status(m)
@test stat == :Optimal
end