Enum Solver 

pub enum Solver {
    Arc,
    Bfgs,
    Efs,
    HybridEfs,
}

Which solver algorithm to use for the outer optimization.

Variants

Arc

Adaptive Regularized Cubic; fastest convergence, requires Hessian.

Bfgs

BFGS; gradient only, builds a dense curvature approximation.

Efs

Extended Fellner-Schall; multiplicative fixed-point iteration. Only valid when all hyperparameter coordinates are penalty-like. Needs no gradient or Hessian — only traces tr(H^{-1} A_k) and Frobenius norms from the inner solution.

HybridEfs

Hybrid EFS + preconditioned gradient.

Used when ψ (design-moving) coordinates are present alongside ρ (penalty-like) coordinates. Combines:

• Standard EFS multiplicative fixed-point steps for ρ coords
• Safeguarded preconditioned gradient steps for ψ coords: Δψ = -α G⁺ g_ψ where G_{de} = tr(H⁻¹ B_d H⁻¹ B_e)

This hybrid exists because no EFS-type fixed-point iteration can guarantee convergence for indefinite B_ψ (proven by counterexample in response.md Section 2). The key structural property that EFS needs — H^{-1/2} B_d H^{-1/2} ≽ 0 plus parameter-independent nullspace — holds for penalty-like coords but fails for design-moving coords where B_ψ has mixed inertia.

The preconditioned gradient uses the same trace Gram matrix that EFS already computes, so the cost is O(1) H⁻¹ solves per iteration (same as pure EFS), compared to O(dim(θ)) for full BFGS.

Trait Implementations

impl Clone for Solver

fn clone(&self) -> Solver

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Solver

impl Debug for Solver

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

Formats the value using the given formatter.

impl Eq for Solver

impl PartialEq for Solver

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for Solver