Add `hs67`

[tmigot]

113

[tmigot]

It misses the JuMP implementation

[codecov[bot]]

Codecov Report

Base: 99.87% // Head: 99.78% // Decreases project coverage by -0.08% :warning:

Coverage data is based on head (c4e6e4d) compared to base (91ac8ce). Patch coverage: 86.66% of modified lines in pull request are covered.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #235 +/- ## ========================================== - Coverage 99.87% 99.78% -0.09% ========================================== Files 766 768 +2 Lines 7011 7056 +45 ========================================== + Hits 7002 7041 +39 - Misses 9 15 +6 ``` | [Impacted Files](https://codecov.io/gh/JuliaSmoothOptimizers/OptimizationProblems.jl/pull/235?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers) | Coverage Δ | | |---|---|---| | [src/Meta/hs67.jl](https://codecov.io/gh/JuliaSmoothOptimizers/OptimizationProblems.jl/pull/235/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers#diff-c3JjL01ldGEvaHM2Ny5qbA==) | `0.00% <0.00%> (ø)` | | | [src/ADNLPProblems/hs67.jl](https://codecov.io/gh/JuliaSmoothOptimizers/OptimizationProblems.jl/pull/235/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers#diff-c3JjL0FETkxQUHJvYmxlbXMvaHM2Ny5qbA==) | `100.00% <100.00%> (ø)` | | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers)

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[tmigot]

[tmigot]

[tmigot]

Hi @odow ! Sorry to bother you, but any chance you would have a suggestion to make a JuMP model for this one?

[odow]

you would have a suggestion to make a JuMP model

Two options jump out:

1. a user-defined function
2. unroll the loop a fixed number of times

let me have a go

[odow]

It's not quite the same, but perhaps:

function yvec(x)
    y = similar(x, 8)
    yc = 1.6x[1]
    while true
        y[2] = yc
        y[3] = 1.22y[2] - x[1]
        y[6] = (x[2] + y[3]) / x[1]
        yc = 0.01x[1] * (112 + 13.167y[6] - 0.6667y[6]^2)
        if abs(yc - y[2]) <= 0.001
            break
        end
    end
    yc = 93
    while true
        y[4] = yc
        y[5] = 86.35 + 1.098y[6] - 0.038y[6]^2 + 0.325(y[4] - 89)
        y[8] = 3y[5] - 133
        y[7] = 35.82 - 0.222y[8]
        yc = 98_000x[3] / (y[2] * y[7] + 1_000x[3])
        if abs(yc - y[4]) <= 0.001
            break
        end
    end
    return y
end

k_iter = 10
a = [0, 0, 85, 90, 3, 0.01, 145, 5_000, 2_000, 93, 95, 12, 4, 162]
using JuMP, Ipopt
model = Model(Ipopt.Optimizer)
x0 = [1_745, 12_000, 110.0]
ub = [2e3, 1.6e4, 1.2e2]
@variable(model, 1e-5 <= x[i=1:3] <= ub[i], start = x0[i])
@variable(model, y[i=1:8, 1:k_iter])
@variable(model, y_actual[i=1:8])
for k in 1:k_iter
    if k == 1
        @constraint(model, y[2, 1] == 1.6x[1])
        @constraint(model, y[4, 1] == 93)
    else
        @NLconstraint(model, y[2, k] == 0.01x[1] * (112 + 13.167y[6, k-1] - 0.6667y[6, k-1]^2))
        @NLconstraint(model, y[4, k] == 98_000x[3] / (y[2, k_iter] * y[7, k-1] + 1_000x[3]))
    end
    @constraint(model, y[3, k] == 1.22y[2, k] - x[1])
    @NLconstraint(model, y[6, k] == (x[2] + y[3, k]) / x[1])
    @constraint(model, y[5, k] == 86.35 + 1.098y[6, k_iter] - 0.038y[6, k_iter]^2 + 0.325(y[4, k] - 89))
    @constraint(model, y[8, k] == 3y[5, k] - 133)
    @constraint(model, y[7, k] == 35.82 - 0.222y[8, k]) 
end
@objective(model, Min, -(0.063y[2, k_iter] * y[5, k_iter] - 5.04x[1] - 3.36y[3, k_iter] - 0.035x[2] - 10x[3]))
@constraint(model, [i=1:7], y[i+1] - a[i] >= 0)
@constraint(model, [i=8:14], a[i] - y[i-6] >= 0)
optimize!(model)
x_sol = value.(x)
y_sol = yvec(x_sol)
x, y = x_sol, y_sol
-(0.063y[2] * y[5] - 5.04x[1] - 3.36y[3] - 0.035x[2] - 10x[3])

JuMP isn't really built for expression graphs of varying size.

[tmigot]

Ok, I get the idea. Thanks for your help!