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

source · `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,

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

source#### pub fn with_tolerance_grad(self, tol_grad: F) -> Result<Self, Error>

#### pub fn with_tolerance_grad(self, tol_grad: F) -> Result<Self, Error>

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>

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

### 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>,

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

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 + ArgminSub<P, P> + ArgminDot<G, H> + ArgminDot<P, H>,
G: Clone + ArgminL2Norm<F> + ArgminMul<F, P> + ArgminDot<P, F> + ArgminSub<G, G>,
H: 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,

### 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 + ArgminSub<P, P> + ArgminDot<G, H> + ArgminDot<P, H>,
G: Clone + ArgminL2Norm<F> + ArgminMul<F, P> + ArgminDot<P, F> + ArgminSub<G, G>,
H: 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§#### fn init(
&mut self,
problem: &mut Problem<O>,
state: IterState<P, G, (), H, (), F>
) -> Result<(IterState<P, G, (), H, (), F>, Option<KV>), Error>

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

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>

`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

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

`terminate_internal`

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

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

## Auto Trait Implementations§

### impl<L, F> RefUnwindSafe for BFGS<L, F>where
F: RefUnwindSafe,
L: RefUnwindSafe,

### impl<L, F> Send for BFGS<L, F>

### impl<L, F> Sync for BFGS<L, F>

### impl<L, F> Unpin for BFGS<L, F>

### impl<L, F> UnwindSafe for BFGS<L, F>where
F: UnwindSafe,
L: 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

§### 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>

`self`

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

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

`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

`self.to_subset`

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

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

`self`

to the equivalent element of its superset.