# Struct argmin::solver::newton::Newton

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

## 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§

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### impl<F> Newton<F>where F: ArgminFloat,

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#### pub fn new() -> Self

Construct a new instance of `Newton`

##### Example
``let newton: Newton<f64> = Newton::new();``
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#### 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§

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

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

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<F> Default for Newton<F>where F: ArgminFloat,

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#### fn default() -> Newton<F>

Returns the “default value” for a type. Read more
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### impl<'de, F> Deserialize<'de> for Newton<F>where F: Deserialize<'de>,

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#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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### impl<F> Serialize for Newton<F>where F: Serialize,

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

Serialize this value into the given Serde serializer. Read more
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### 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,

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#### const NAME: &'static str = "Newton method"

Name of the solver. Mainly used in Observers.
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#### 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.
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#### fn terminate_internal(&mut self, state: &I) -> TerminationStatus

Checks whether basic termination reasons apply. Read more
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#### fn terminate(&mut self, _state: &I) -> TerminationStatus

Used to implement stopping criteria, in particular criteria which are not covered by (`terminate_internal`. Read more
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## Blanket Implementations§

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### impl<T> Any for Twhere T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> ToOwned for Twhere T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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