# Struct argmin::solver::quasinewton::BFGS

``pub struct BFGS<L, F> { /* private fields */ }``
Expand description

## BFGS method

The Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) is a method for solving unconstrained nonlinear optimization problems.

The algorithm requires a line search which is provided via the constructor. Additionally an initial guess for the parameter vector and an initial inverse Hessian is required, which are to be provided via the `configure` method of the `Executor` (See `IterState`, in particular `IterState::param` and `IterState::inv_hessian`). In the same way the initial gradient and cost function corresponding to the initial parameter vector can be provided. If these are not provided, they will be computed during initialization of the algorithm.

Two tolerances can be configured, which are both needed in the stopping criteria. One is a tolerance on the gradient (set with `with_tolerance_grad`): If the norm of the gradient is below said tolerance, the algorithm stops. It defaults to `sqrt(EPSILON)`. The other one is a tolerance on the change of the cost function from one iteration to the other. If the change is below this tolerance (default: `EPSILON`), the algorithm stops. This parameter can be set via `with_tolerance_cost`.

### Requirements on the optimization problem

The optimization problem is required to implement `CostFunction` and `Gradient`.

### Reference

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

## Implementations§

source§

### impl<L, F> BFGS<L, F>where F: ArgminFloat,

source

#### pub fn new(linesearch: L) -> Self

Construct a new instance of `BFGS`

##### Example
``let bfgs: BFGS<_, f64> = BFGS::new(linesearch);``
source

The algorithm stops if the norm of the gradient is below `tol_grad`.

The provided value must be non-negative. Defaults to `sqrt(EPSILON)`.

##### Example
``let bfgs: BFGS<_, f64> = BFGS::new(linesearch).with_tolerance_grad(1e-6)?;``
source

#### pub fn with_tolerance_cost(self, tol_cost: F) -> Result<Self, Error>

Sets tolerance for the stopping criterion based on the change of the cost stopping criterion

The provided value must be non-negative. Defaults to `EPSILON`.

##### Example
``let bfgs: BFGS<_, f64> = BFGS::new(linesearch).with_tolerance_cost(1e-6)?;``

## Trait Implementations§

source§

### impl<L: Clone, F: Clone> Clone for BFGS<L, F>

source§

#### fn clone(&self) -> BFGS<L, F>

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from `source`. Read more
source§

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

source§

#### 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<L, F> Serialize for BFGS<L, F>where L: Serialize, F: Serialize,

source§

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

Serialize this value into the given Serde serializer. Read more
source§

### impl<O, L, P, G, H, F> Solver<O, IterState<P, G, (), H, F>> for BFGS<L, F>where O: CostFunction<Param = P, Output = F> + Gradient<Param = P, Gradient = G>, P: Clone + SerializeAlias + DeserializeOwnedAlias + ArgminSub<P, P> + ArgminDot<G, H> + ArgminDot<P, H>, G: Clone + SerializeAlias + DeserializeOwnedAlias + ArgminL2Norm<F> + ArgminMul<F, P> + ArgminDot<P, F> + ArgminSub<G, G>, H: SerializeAlias + DeserializeOwnedAlias + ArgminSub<H, H> + ArgminDot<G, G> + ArgminDot<H, H> + ArgminAdd<H, H> + ArgminMul<F, H> + ArgminTranspose<H> + ArgminEye, L: Clone + LineSearch<P, F> + Solver<O, IterState<P, G, (), (), F>>, F: ArgminFloat,

source§

#### const NAME: &'static str = "BFGS"

Name of the solver. Mainly used in Observers.
source§

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>

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 terminate(&mut self, state: &IterState<P, G, (), H, F>) -> TerminationStatus

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

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

Checks whether basic termination reasons apply. Read more

§

§

§

§

§

## Blanket Implementations§

source§

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

source§

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

Gets the `TypeId` of `self`. Read more
source§

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

const: unstable · source§

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

Immutably borrows from an owned value. Read more
source§

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

const: unstable · source§

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

Mutably borrows from an owned value. Read more
source§

### impl<T> From<T> for T

const: unstable · source§

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

Returns the argument unchanged.

source§

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

const: unstable · source§

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

Calls `U::from(self)`.

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

source§

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

§

#### type Owned = T

The resulting type after obtaining ownership.
source§

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

Creates owned data from borrowed data, usually by cloning. Read more
source§

#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
source§

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

§

#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
source§

### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

§

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

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
§

§

source§

source§