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optimizer.jl
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optimizer.jl
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using DifferentialEquations
using Plots
using Plotly
using JuMP
using Ipopt
using GLPK
using ProgressBars
using LaTeXStrings
#plotly()
gr()
include("newaux.jl")
g0 = SIRS_Game(2,fp)
g0.x_star
g0.σ = 0.1
g0.ω = 0.005
g0.γ = g0.σ
g0.υ = 2.0
g0.β = [0.15;0.19]
g0.c = [0.2;0.0]
g0.c_star = 0.1
g0.ρ = 0.0
fixall!(g0)
I = Ib(g0,g0.β[1])
R = Rb(g0,g0.β[1])
S = 1.0-I-R
W = [g0.β[1]*I;g0.β[1]*R;1.0;0.0]
## assertions
# betas are in increasing order
@assert all(diff(g0.β).>0)
# c vector is in decreasing order
@assert all(diff(g0.c).<0)
# σ < β[1]
@assert all(g0.σ.<g0.β)
#c_star > g0.c[end]
@assert g0.c_star>g0.c[end]
##
## Figure 1
#solution using nonlinear programming
T = exp.(range(-5,stop=0,length=10))
bounds_list = []
optimal_list = []
fixall!(g0)
for g0.υ = ProgressBar(T)
for g0.β_star ∈ [0.16, 0.17, 0.18]
β̃ = abs(g0.β[1]-g0.β_star)
#fixall!(g0)
α = 0.5*(g0.υ*β̃ )^2
m = Model(Ipopt.Optimizer)
set_optimizer_attribute(m, "tol", 1e-12)
set_optimizer_attribute(m, "acceptable_tol", 1e-12)
set_optimizer_attribute(m, "dual_inf_tol", 1e-12)
set_optimizer_attribute(m, "acceptable_constr_viol_tol", 1e-12)
set_optimizer_attribute(m, "bound_relax_factor", 0.0)
set_optimizer_attribute(m, "mu_init", 1e-1)
set_optimizer_attribute(m, "gamma_theta", 1e-2)
set_optimizer_attribute(m, "honor_original_bounds", "yes")
set_optimizer_attribute(m, "max_iter", 10000)
set_silent(m)
@variable(m, I >= 0)
@variable(m, R >= 0)
@variable(m, maximum(g0.β) >= B >= minimum(g0.β))
@constraint(m, R+I<=B)
@NLconstraint(m, (I-g0.η*(B-g0.σ))+g0.η*(B-g0.σ)*log(g0.η*(B-g0.σ)/I)+(R-(1-g0.η)*(B-g0.σ))^2/(2*g0.γ)+g0.υ^2*(B-g0.β_star)^2/2<=α )
@NLobjective(m, Max, I/B )
optimize!(m)
up_bd = objective_value(m)/(g0.η*(1-g0.σ/g0.β_star))
#println("$(value(B)) $(g0.υ) ")
push!(optimal_list, primal_status(m))
#=β_star
@NLobjective(m, Max, (-I+g0.η*(g0.β_star-g0.σ))/B )
optimize!(m)
lo_bd = objective_value(m)
=#
#push!(bounds_list, [β̃ ,g0.υ,max(lo_bd,up_bd)])
push!(bounds_list, [g0.β_star,g0.υ,max(0,up_bd)])
push!(optimal_list, primal_status(m))
if termination_status(m) != JuMP.MOI.LOCALLY_SOLVED
print(termination_status(m))
print(m)
end
end
end
bounds_list_aux = bounds_list
bounds_list_aux = permutedims(hcat(bounds_list_aux...))
Plots.plot()
for i in unique(bounds_list_aux[:,1])
aux = bounds_list_aux[bounds_list_aux[:,1].==i,2:3]
Plots.plot!( aux[:,1], aux[:,2], label=L"β^*="*"$(round(i,digits=4))", title=" υ vs π* ", xlabel="υ", ylabel=L"\pi_\upsilon^*\left(0.5 \upsilon^2 \tilde{\beta}^2\right)", legend=:outerright)
end
Plots.plot!() #xaxis=:log,yaxis=:log
#println(optimal_list)
##
Plots.savefig("images/NLP_alpha_vs_pi_star")
#solution using feasibility check of convex programs
##this works too, but it is way slower than the approach above
#=
bounds_list = []
optimal_list = []
for g0.υ = ProgressBar([0.001,0.01,0.06,0.1,0.3,1.0,10.0,100.0])
fixall!(g0)
for α = ProgressBar(T)
l_0 = 1.0
l_1 = 0.0
p = (l_0+l_1)/2
m = Model(Ipopt.Optimizer)
set_silent(m)
@variable(m, I >= 0)
@variable(m, g0.β[2] >= B >= g0.β[1])
@variable(m, R >= 0)
@constraint(m, I+R<=B)
@objective(m, Max, 1 )
@NLconstraint(m, (I-g0.η*(B-g0.σ))+g0.η*(B-g0.σ)*log(g0.η*(B-g0.σ)/I)+(R-(1-g0.η)*(B-g0.σ))^2/(2*g0.γ)+g0.υ*(B-g0.β_star)^2/2<=α )
g = p
myconstr = @constraint(m, g*B<=(-I+g0.η*(g0.β_star-g0.σ)))
for nnnn=1:10
g = p
delete(m, myconstr)
myconstr = @constraint(m, g*B<=(-I+g0.η*(g0.β_star-g0.σ)))
optimize!(m)
#println("$(p) $(primal_status(m))")
if (primal_status(m)==MOI.FEASIBLE_POINT)
l_0 = l_0
l_1 = p
else
l_0 = p
l_1 = l_1
end
p = (l_0+l_1)/2
if l_0-l_1<1e-4
break
end
end
#println("$(p) $(primal_status(m))")
#println("sdfsdfsdf")
l_0 = 1.0
l_1 = 0.0
n = (l_0+l_1)/2
g = n
for nnnn=1:10
g = n
delete(m, myconstr)
myconstr = @constraint(m, g*B<=(I-g0.η*(g0.β_star-g0.σ)))
optimize!(m)
#println("n = $n stat $(primal_status(m))")
if (primal_status(m)==MOI.FEASIBLE_POINT)
l_0 = l_0
l_1 = n
else
l_0 = n
l_1 = l_1
end
n = (l_0+l_1)/2
if l_0-l_1<1e-4
break
end
end
#println("$(n) $(primal_status(m))")
push!(bounds_list, [g0.υ ,α,max(p,n)])
end
end
bounds_list = permutedims(hcat(bounds_list...))
Plots.plot()
for i in unique(bounds_list[:,1])
aux = bounds_list[bounds_list[:,1].==i,2:3]
Plots.plot!( aux[:,1], aux[:,2], label="υ=$i", title="α vs π* ", xlabel="α", ylabel="π*")
end
Plots.plot!()
#println(optimal_list)
Plots.savefig("QuasiCP_alpha_vs_pi_star")
## They should give us the same results
=#
##