pub fn natural_residual(
inp: &CertificateInput<'_>,
) -> Option<(Number, Vec<HeldSide>)>Expand description
The largest natural residual min(|G_k|, |H_k|) over the pairs at a
point, with the branch that removes it: each pair’s smaller side held at
zero. A mixed pair is read as the one-sided pair of its nearer bound, as
the certificate reads it.
Every stage stops at a pair product near the last τ, which is harmless
where a pair is strictly complementary (the other side is O(1), so the
smaller is ≈ τ) and is not where a pair is nearly biactive: there both
sides sit near sqrt(τ). On MPCCModels.jl’s OPF volt-var cases (PR #13)
the answer at a curve knot had r = 7.8e-5, s = 1.3e-4 at a product of
1e-8, the curve’s slope of 7.5 put Q 5.9e-4 off it, and the objective
read better than the model’s true optimum by what that slack bought.
None with no pairs or a non-finite side.