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copositive_simplex_minimum

Function copositive_simplex_minimum 

Source
pub fn copositive_simplex_minimum(
    matrix: ArrayView2<'_, f64>,
) -> Result<(f64, Array1<f64>), String>
Expand description

Exact minimum of wᵀMw over the unit simplex {w ≥ 0, 1ᵀw = 1}.

Strictly positive iff M is strictly copositive, which is exactly the condition for exp(−½wᵀMw) to be normalizable on a shifted orthant. On the face with support S the stationary value is 1/(1ᵀM_SS⁻¹1), so enumerating all 2ⁿ − 1 supports and the vertices M_jj decides it — no nonconvex QP, and a non-positive answer is a PROOF of impropriety rather than an inconclusive bound.