`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§

## Trait Implementations§

source§### impl<F> Default for Newton<F>where
F: ArgminFloat,

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

source§### impl<'de, F> Deserialize<'de> for Newton<F>where
F: Deserialize<'de>,

### impl<'de, F> Deserialize<'de> for Newton<F>where
F: Deserialize<'de>,

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

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

Deserialize this value from the given Serde deserializer. Read more

source§### 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,

### 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,

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

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

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

Initializes the algorithm. Read more

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

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

Checks whether basic termination reasons apply. Read more

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

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

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

`terminate_internal`

. Read more### impl<F: Copy> Copy for Newton<F>

## Auto Trait Implementations§

### impl<F> RefUnwindSafe for Newton<F>where
F: RefUnwindSafe,

### impl<F> Send for Newton<F>where
F: Send,

### impl<F> Sync for Newton<F>where
F: Sync,

### impl<F> Unpin for Newton<F>where
F: Unpin,

### impl<F> UnwindSafe for Newton<F>where
F: UnwindSafe,

## Blanket Implementations§

source§### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

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

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

Mutably borrows from an owned value. Read more

§### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

§#### fn to_subset(&self) -> Option<SS>

#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct

`self`

from the equivalent element of its
superset. Read more§#### fn is_in_subset(&self) -> bool

#### fn is_in_subset(&self) -> bool

Checks if

`self`

is actually part of its subset `T`

(and can be converted to it).§#### fn to_subset_unchecked(&self) -> SS

#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as

`self.to_subset`

but without any property checks. Always succeeds.§#### fn from_subset(element: &SS) -> SP

#### fn from_subset(element: &SS) -> SP

The inclusion map: converts

`self`

to the equivalent element of its superset.