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Second order correction #8

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Second order correction #8

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a8c0f64
versão para rodar o CUTEst
Apr 22, 2020
5aad1cd
second order correction
May 25, 2020
2a6b667
changes in mu, merit function, SOC for new test in CUTEst
rodrigosgr Jul 9, 2020
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3 changes: 3 additions & 0 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -9,6 +9,9 @@ Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
NLPModels = "a4795742-8479-5a88-8948-cc11e1c8c1a6"
NLPModelsIpopt = "f4238b75-b362-5c4c-b852-0801c9a21d71"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
SolverTools = "b5612192-2639-5dc1-abfe-fbedd65fab29"
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
165 changes: 79 additions & 86 deletions src/SQP.jl
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Original file line number Diff line number Diff line change
@@ -1,28 +1,24 @@
module SQP

module SQP

export sqp


using LinearAlgebra
using Krylov
using NLPModels
using SolverTools
using JSOSolvers


function sqp(nlp :: AbstractNLPModel;
x :: AbstractVector = copy(nlp.meta.x0),
atol :: Real = sqrt(eps(eltype(x))),
rtol :: Real = sqrt(eps(eltype(x))),
max_eval :: Int = -1,
max_iter :: Int = 25,
max_iter :: Int = 1000,
max_time :: Float64 = 30.0,
relax_param :: Float64 = 0.6,
trust_reg :: Float64 = 1.0,
μ0 :: Float64 = 1.0)


if bound_constrained(nlp)
return tron(nlp, x = copy(nlp.meta.x0), max_time = max_time, atol = atol, rtol = rtol, max_eval = max_eval)
end
Expand All @@ -39,21 +35,19 @@ function sqp(nlp :: AbstractNLPModel;
start_time = time()
n = nlp.meta.nvar
m = nlp.meta.ncon
y = copy(nlp.meta.y0)
fx = obj(nlp, x)
cx = cons(nlp, x) - nlp.meta.ucon
gx = grad(nlp, x)
A = jac(nlp, x)
LSMR_dual = lsmr(A', gx)
y = LSMR_dual[1]
maior_y = norm(y, Inf)
W = Symmetric(hess(nlp, x, y), :L)
Z = nullspace(Matrix(A))
norm_cx = norm(cx)
tr = TrustRegion(trust_reg)
ρ = 0.0
μ = μ0
last_accepted_μ = μ0 # for the first iteration
last_accepted_norm_c = norm_cx
last_rejected = false # the information from the last two steps is needed for the μ update
last_but_one_rejected = false

exitflag = :unknow
dual = A'*y - gx
Expand All @@ -65,7 +59,7 @@ function sqp(nlp :: AbstractNLPModel;
Δt = time() - start_time
tired = Δt > max_time || iter > max_iter || neval_obj(nlp) > max_eval > 0
if tired
if Δt > max_time
if Δt > max_time
exitflag = :max_time
elseif iter > max_iter
exitflag = :max_iter
Expand All @@ -78,91 +72,93 @@ function sqp(nlp :: AbstractNLPModel;
@info log_row(Any[iter, Δt, normdual, norm_cx, tr.radius, ρ])

while !(success || tired)
v = lsmr(A, -cx, radius = relax_param * tr.radius, atol = atol, rtol = rtol, itmax = max(2 * n, 50))[1]
ZWZ = Z' * W * Z
LSMR = lsmr(A, -cx, radius = relax_param * tr.radius, atol = atol, rtol = rtol, itmax = max(2 * n, 50))
v = LSMR[1]
ZWZ = Z' * W * Z
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Suggested change
ZWZ = Z' * W * Z
ZWZ = Z' * W * Z

ZWv = Z' * (W*v + gx)
u = cg(ZWZ, -ZWv, radius = sqrt(tr.radius^2 - norm(v)^2), atol = atol, rtol = 0.0, itmax = max(2 * n, 50))[1]
Zu = Z * u
CG = cg(ZWZ, -ZWv, radius = sqrt(tr.radius^2 - norm(v)^2), atol = atol, rtol= 0.0, itmax = max(2 * n, 50))
u = CG[1]
Zu = Z * u
d = v + Zu
norm_v = norm(v)
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Suggested change
CG = cg(ZWZ, -ZWv, radius = sqrt(tr.radius^2 - norm(v)^2), atol = atol, rtol= 0.0, itmax = max(2 * n, 50))
u = CG[1]
Zu = Z * u
d = v + Zu
norm_v = norm(v)
CG = cg(ZWZ, -ZWv, radius = sqrt(tr.radius^2 - norm(v)^2), atol = atol, rtol= 0.0, itmax = max(2 * n, 50))
u = CG[1]
Zu = Z * u
d = v + Zu
norm_v = norm(v)


next_x = x + d
next_f = obj(nlp, next_x)
next_c = cons(nlp, next_x) - nlp.meta.ucon
next_norm_c = norm(next_c)
next_norm_c = norm(next_c, 1)
vpred = norm_cx - norm(A*v + cx)
upred = 0.5 * (u'*ZWZ*u)[1] + dot(ZWv,u)
μ_bar = 0.1 + upred / vpred # auxiliary variable for μ update

μ_plus = max(μ, μ_bar) # another auxiliary variable
if μ_plus > μ && μ_plus < 5 * μ && μ > last_accepted_μ && norm_cx > 0.2 * last_accepted_norm_c && (last_rejected || last_but_one_rejected)
μ_plus = min(5 * μ, μ_plus + 25 * (μ_plus - last_accepted_μ))
end
if μ_plus == μ && norm(v) < relax_param * tr.radius/10 && norm_cx < 1e4 * atol
μ_plus = max(μ0, μ_bar, norm(y))
D = dot(d, gx)
dWd = (d'*W*d)[1]
dpred = 0.5 * dWd + D

μ_bar = maior_y + 0.1
if(dWd >= 0)
if(μ > μ_bar)
μ_plus = μ
else
μ_plus = μ_bar
end
else
μ_plus = μ_bar - dWd / norm_cx
end

#ϕ(x) = obj(nlp, x) + μ_plus * norm(cons(nlp, x))
#nlp_aux = ADNLPModel(ϕ, x)
ϕx = fx + μ_plus * norm_cx
ϕn = next_f + μ_plus * next_norm_c
Δm = μ * vpred - upred
μ = max(μ_plus, dpred / (0.7 * vpred) + 0.1)

ϕx = fx + μ * norm_cx
ϕn = next_f + μ * next_norm_c
Δm = μ * vpred - dpred
μ_norm_cx = μ * norm_cx
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Suggested change
μ_norm_cx = μ * norm_cx
μ_norm_cx = μ * norm_cx


ared, pred = aredpred(nlp, ϕn, ϕx, Δm, next_x, d, dot(d, gx) - μ_plus * norm_cx)
ared, pred = aredpred(nlp, ϕn, ϕx, Δm, next_x, d, D - μ_norm_cx)
ρ = ared / pred
set_property!(tr, :ratio, ρ)

norm_v = norm(v)
norm_Zu = norm(Zu)


if acceptable(tr)
x = next_x
fx = next_f
cx = next_c
norm_cx = next_norm_c
A = jac(nlp, x)
gx = grad(nlp, x)
y = lsmr(A', gx)[1]
W = Symmetric(hess(nlp, x, y), :L)
Z = nullspace(Matrix(A))
last_but_one_rejected = last_rejected
last_rejected = false
last_accepted_μ = μ
last_accepted_norm_c = norm_cx
elseif norm_v < 0.8 * relax_param * tr.radius && norm_v < 0.1 * norm_Zu
aux_sist = cg(A*A', next_c)[1]
d -= A'*aux_sist
next_x = x + d
next_f = obj(nlp, next_x)
next_cx = cons(nlp, next_x) - nlp.meta.ucon
next_norm_c = norm(next_cx)
ϕx = fx + μ_plus * norm_cx
ϕn = next_f + μ_plus * next_norm_c
Δm = μ * vpred - upred
ared, pred = aredpred(nlp, ϕn, ϕx, Δm, next_x, d, dot(d, gx) - μ_plus * norm_cx)
ρ = ared / pred
set_property!(tr, :ratio, ρ)
x = next_x
fx = next_f
cx = next_c
norm_cx = next_norm_c
A = jac(nlp, x)
gx = grad(nlp, x)
y = lsmr(A', gx)[1]
W = Symmetric(hess(nlp, x, y), :L)
Z = nullspace(Matrix(A))
last_but_one_rejected = last_rejected
last_rejected = false
last_accepted_μ = μ
last_accepted_norm_c = norm_cx
else
last_but_one_rejected = last_rejected
last_rejected = true
normv = norm(v)
normu = norm(Zu)

if acceptable(tr)
x = next_x
fx = next_f
cx = next_c
norm_cx = next_norm_c
A = jac(nlp, x)
gx = grad(nlp, x)
LSMR_dual = lsmr(A', gx)
y = LSMR_dual[1]
W = Symmetric(hess(nlp, x, y), :L)
Z = nullspace(Matrix(A))
elseif (normv <= 0.1 * normu) && (normv <= 0.8 * relax_param * tr.radius)
LSMR_aux = lsmr(A, next_c, atol = atol, rtol = rtol)
w = LSMR_aux[1]
d_soc = d + w
next_x = x + d_soc
next_f = obj(nlp, next_x)
next_cx = cons(nlp, next_x) - nlp.meta.ucon
next_norm_c = norm(next_cx)
ϕx = fx + μ * norm_cx
ϕn = next_f + μ * next_norm_c
D = dot(d_soc, gx)
Δm = μ * (norm_cx - norm(A*d_soc + cx)) - 0.5 * (d_soc'*W*d_soc)[1] - D

ared, pred = aredpred(nlp, ϕn, ϕx, Δm, next_x, d, D - μ_norm_cx)
ρ = ared / pred
set_property!(tr, :ratio, ρ)

if acceptable(tr)
x = next_x
fx = next_f
cx = next_c
norm_cx = next_norm_c
A = jac(nlp, x)
gx = grad(nlp, x)
LSMR_dual = lsmr(A', gx)
y = LSMR_dual[1]
W = Symmetric(hess(nlp, x, y), :L)
Z = nullspace(Matrix(A))
end
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Diversos lugares acima. Por favor use um editor que permite a substituição de TAB por espaços ou faça manualmente.

end

μ = μ_plus

update!(tr, norm(d))

update!(tr, norm(d, 2))
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Suggested change
update!(tr, norm(d, 2))
update!(tr, norm(d))

Por padrão é a 2.


dual = A'*y - gx
normdual = norm(dual)
Expand All @@ -184,14 +180,11 @@ function sqp(nlp :: AbstractNLPModel;
end

@info log_row(Any[iter, Δt, normdual, norm_cx, tr.radius, ρ])

end

cx = cx + nlp.meta.ucon

return GenericExecutionStats(exitflag, nlp, solution = x, objective = fx, dual_feas = normdual, primal_feas = norm_cx, iter = iter, elapsed_time = Δt)

end


end # module