Struct Newton

pub struct Newton<F> { /* private fields */ }

Newton’s method

Newton’s method iteratively finds the stationary points of a function f by using a second order approximation of f at the current point.

The stepsize gamma can be adjusted with the with_gamma method. It must be in (0, 1]) and defaults to 1.

Requirements on the optimization problem

The optimization problem is required to implement Gradient and Hessian.

Reference

Jorge Nocedal and Stephen J. Wright (2006). Numerical Optimization. Springer. ISBN 0-387-30303-0.

Implementations

impl<F> Newton<F>

where F: ArgminFloat,

pub fn new() -> Self

Construct a new instance of Newton

Example

let newton: Newton<f64> = Newton::new();

pub fn with_gamma(self, gamma: F) -> Result<Self, Error>

Set step size gamma

Gamma must be in (0, 1] and defaults to 1.

Example

let newton: Newton<f64> = Newton::new().with_gamma(0.4)?;

Trait Implementations

impl<F: Clone> Clone for Newton<F>

fn clone(&self) -> Newton<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> Default for Newton<F>

where F: ArgminFloat,

fn default() -> Newton<F>

Returns the “default value” for a type.

impl<'de, F> Deserialize<'de> for Newton<F>

where F: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F> Serialize for Newton<F>

where F: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<O, P, G, H, F> Solver<O, IterState<P, G, (), H, (), F>> for Newton<F>

where O: Gradient<Param = P, Gradient = G> + Hessian<Param = P, Hessian = H>, P: Clone + ArgminScaledSub<P, F, P>, H: ArgminInv<H> + ArgminDot<G, P>, F: ArgminFloat,

fn name(&self) -> &str

Name of the solver. Mainly used in Observers.

fn next_iter( &mut self, problem: &mut Problem<O>, state: IterState<P, G, (), H, (), F>, ) -> Result<(IterState<P, G, (), H, (), F>, Option<KV>), Error>

Computes a single iteration of the algorithm and has access to the optimization problem definition and the internal state of the solver. Returns an updated state and optionally a KV which holds key-value pairs used in Observers.

fn init( &mut self, _problem: &mut Problem<O>, state: I, ) -> Result<(I, Option<KV>), Error>

Initializes the algorithm.

fn terminate_internal(&mut self, state: &I) -> TerminationStatus

Checks whether basic termination reasons apply.

fn terminate(&mut self, _state: &I) -> TerminationStatus

Used to implement stopping criteria, in particular criteria which are not covered by (terminate_internal.

impl<F: Copy> Copy for Newton<F>