Struct RiemannianTrustRegion 

pub struct RiemannianTrustRegion {
    pub radius: f64,
    pub max_radius: f64,
    pub max_iter: usize,
    pub grad_tol: f64,
}

Fields

radius: f64

Initial trust-region radius Δ₀.

max_radius: f64

Hard cap Δmax on the radius across all iterations.

max_iter: usize

grad_tol: f64

Implementations

impl RiemannianTrustRegion

pub fn minimize( &self, manifold: &dyn RiemannianManifold, objective: &mut dyn RiemannianObjective, initial: ArrayView1<'_, f64>, ) -> GeometryResult<Array1<f64>>

A genuine Riemannian trust-region method.

At each iterate x we build the quadratic model in the tangent space T_xM,

  m(η) = f(x) + g_x(grad, η) + ½ g_x(η, Hη),

where g_x(·,·) is the manifold metric inner product and H is the Riemannian Hessian (accessed only through Hessian–vector products). The step is the (approximate) solution of the trust-region subproblem

  min_{η ∈ T_xM, ‖η‖_g ≤ Δ}  m(η).

When the objective supplies Hessian–vector products AND the manifold’s retract is at least a second-order retraction (RiemannianManifold::retraction_is_second_order) we solve the subproblem with the Steihaug truncated-CG method (stopping at negative curvature or the trust-region boundary). Otherwise — no curvature, or a first-order retraction whose pullback second derivative is not the Riemannian Hessian (issue #956) — we fall back to the Cauchy point: the exact minimizer of the model along the steepest-descent direction within the trust region (with curvature taken from the model where available, and the boundary point of the decreasing linear model otherwise). The linear term Df_x[η] is retraction-independent, so the Cauchy model keeps ρ and the radius control valid along any retraction. Either way this is a real model-based step — not clipped descent.

We then form the ratio of actual to predicted reduction

  ρ = (f(x) − f(x⁺)) / (m(0) − m(η)),

accept the step only when ρ > η₁, and adapt Δ: shrink on a poor ratio, expand on an excellent ratio that reaches the boundary, otherwise hold. Only accepted steps are retracted onto the manifold.

Trait Implementations

impl Clone for RiemannianTrustRegion

fn clone(&self) -> RiemannianTrustRegion

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for RiemannianTrustRegion

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

Formats the value using the given formatter.

impl Default for RiemannianTrustRegion

fn default() -> Self

Returns the “default value” for a type.

impl PartialEq for RiemannianTrustRegion

fn eq(&self, other: &RiemannianTrustRegion) -> 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 RiemannianTrustRegion