Struct Regularization 

pub struct Regularization<T: Real = f64> {
    pub primal: T,
    pub dual: T,
    pub pivot_tol: Option<T>,
    pub bump: T,
    pub scale: ShiftScale,
}

Regularization of a quasi-definite KKT matrix (Altman & Gondzio 1999; Algorithm K).

Fields

primal: T

ρ ≥ 0, added to the primal block (which becomes −D − ρI, in the units Regularization::scale says); ignored for the normal equations.

dual: T

δ ≥ 0, added to the dual block (δI), or to the whole diagonal of the normal equations (A D Aᵀ + δI), in the units Regularization::scale says.

pivot_tol: Option<T>

Below this magnitude (or with the wrong sign) a pivot of the equilibrated matrix is bumped to ±bump with the sign the inertia expects (dynamic regularization, step K3); None disables it.

bump: T

The magnitude β > 0 of a bumped pivot (of the equilibrated matrix).

scale: ShiftScale

Whether ρ, δ are taken in the equilibrated matrix (the default) or in K itself (step K2″).

Implementations

impl<T: Real> Regularization<T>

pub fn none() -> Self

No regularization at all: ρ = δ = 0, no bumping (the factorization then fails on a zero pivot, or with the wrong inertia).

pub fn relative_to(k: &CscMatrix<T>, factor: T) -> Self

Absolute static shifts relative to the largest entry of k: ρ = δ = factor · max|k_ij| with ShiftScale::Absolute, and the dynamic part of Regularization::default (the L1.5 variant).

One shift for the whole matrix: at the end of an interior-point method, where max|k_ij| ≈ 10^{10}, factor = 10⁻⁸ gives δ ≈ 10², a large perturbation of the rows of small magnitude — refinement against the unregularized K then converges slowly (Chapter 5.14, “Choosing the regularization”). The default (ShiftScale::Equilibrated) is relative row by row instead.

pub fn is_quasi_definite(&self) -> bool

ρ > 0 and δ > 0: the regularized augmented matrix is quasi-definite (it factorizes without pivoting, in any order).

Trait Implementations

impl<T: Clone + Real> Clone for Regularization<T>

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Copy + Real> Copy for Regularization<T>

impl<T: Debug + Real> Debug for Regularization<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Real> Default for Regularization<T>

fn default() -> Self

ρ = 10⁻⁶, δ = 10⁻⁸ in the equilibrated matrix (ShiftScale::Equilibrated: relative to each row), and pivots of the wrong sign or of magnitude at most τ = 10⁻¹³ bumped to ±β = ±2·10⁻⁷. ρδ = 10⁻¹⁴, about 50 units of roundoff, keeps the regularized augmented matrix numerically quasi-definite; δ alone, small, is what the normal equations see (Chapter 5.14, “Choosing the regularization”, measured in L1.5b). τ, β are of the order of the defaults of current interior-point codes (Clarabel’s documented dynamic regularization; not tuned here).

impl<T: PartialEq + Real> PartialEq for Regularization<T>

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl<T: PartialEq + Real> StructuralPartialEq for Regularization<T>