Struct mathru::optimization::Gradient

pub struct Gradient<T> { /* fields omitted */ }

Gradient method

It is assumed that $f \colon D \in \mathbb{R}^n \to \mathbb{R}$ The idea is, that in every iteration a step is made in direction of the anti gradient.

x_{k + 1} := x_{k} - \alpha_{k} \nabla f(x_{k})

in order that $f(x_{k + 1}) < f(x_{k})$.

input: Function $f: \mathbb{R}^n \to \mathbb{R}$, and initial approximation $x_{0} \in \mathbb{R}^{n}$

output: $x_{k}$

1. Initialization: choose $\sigma \in (0, 1) $

   set $k := 0 $

2. calculate antigradient $d_{k} := -\nabla f(x_{k}) $

   set $\alpha_{k} := 1$

3. while $f(x_{k} + \alpha_{k} d_{k}) > f(x_k) + \sigma \alpha_{k} \lvert \lvert d_{k} \rvert \rvert_{2}^{2} $ set $\alpha_{k} := \alpha_{k} /2$ 4. $x_{k + 1} := x_{k} + \alpha_{k} d_{k}$

4. $k := k + 1$ go to 2.

Implementations

impl<T> Gradient<T> where
    T: Real, 

pub fn new(sigma: T, iters: usize) -> Gradient<T>

Construct an instance of gradient algorithm.

Parameters

sigma: learning rate > 0.0

Examples

use mathru::optimization::Gradient;

let gd = Gradient::new(0.3, 10000);

impl<T> Gradient<T> where
    T: Real, 

pub fn minimize<F>(&self, func: &F, x_0: &Vector<T>) -> OptimResult<Vector<T>> where
    F: Optim<T>, 

Trait Implementations

impl<T: Clone> Clone for Gradient<T>

pub fn clone(&self) -> Gradient<T>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Copy> Copy for Gradient<T>

impl<T: Debug> Debug for Gradient<T>

pub fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<'de, T> Deserialize<'de> for Gradient<T> where
    T: Deserialize<'de>, 

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

Deserialize this value from the given Serde deserializer.

impl<T> Serialize for Gradient<T> where
    T: Serialize, 

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

Serialize this value into the given Serde serializer.