Differentiation of problems with Almost Locally Solved termination status

[awest32]

DiffOpt seems to not suppoer problems with the termination status Almost Locally Solved. Below is a minimum working example.

using JuMP
using Ipopt
using DiffOpt

# Create differentiable model with loose tolerances
diff_optimizer = optimizer_with_attributes(
    Ipopt.Optimizer,
    "print_level" => 3,
    "tol" => 1e-2,
    "acceptable_tol" => 1e-1,
    "max_iter" => 5,
    "acceptable_iter" => 2
)

model = Model(() -> DiffOpt.diff_optimizer(diff_optimizer))

# Decision variables
@variable(model, x >= 0)
@variable(model, y >= 0)

# Parameters (weights in objective)
w = [0.1, 0.1]  # Initial parameter values
weight = w
weight = JuMP.@variable(
    model,
    [j in keys(w)] in MOI.Parameter(w[j]),
    base_name = "weight")

@constraint(model, x + y >= 10)
@constraint(model, 2x + y >= 15)

@objective(model, Min, weight[1]*x + weight[2]*y)

optimize!(model)

println("\nStatus: $(termination_status(model))")

for (i, key) in enumerate(keys(weight))
    perturbation = i
    DiffOpt.set_forward_parameter(model, weight[key], perturbation)
end

# Solve perturbed problem
optimize!(model)

# Compute forward derivatives
DiffOpt.forward_differentiate!(model)

[andrewrosemberg]

From our chat, we should perhaps include this, or at least make checking an attribute.

Don't remember if Almost Locally Solved always guarantees to return primal and dual.

[odow]

Almost Locally Solved always guarantees to return primal and dual

This is never true, even if the status is MOI.OPTIMAL. You must always check for FEASIBLE_POINT (or NEARLY_FEASIBLE_POINT)

[andrewrosemberg]

I now remember why we added the check; indeed it was not because of solution availability, but to avoid silently calculating sensitivities that perhaps didn't make sense. Checking OPTIMAL or Local Solved was a proxy for some regularity conditions.

Perhaps this is not the best way to do it, and we should leave it to the user to check before they query the sensitivity. I am ok removing the check altogether if no one opposes.

[joaquimg]

We can remove check, but add a warning.
The warning could be disabled by a parameter.