Struct mathru::optimization::Gradient

pub struct Gradient { /* 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. $x_{k + 1} := x_{k} + \alpha_{k} d_{k}$

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

Methods

impl Gradient

pub fn new(sigma: f64, iters: usize) -> Gradient

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 Gradient

pub fn minimize<F: Jacobian<f64>>(
    &self,
    func: &F,
    x_0: &Vector<f64>
) -> OptimResult<Vector<f64>>

Trait Implementations

impl Clone for Gradient

fn clone(&self) -> Gradient

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Copy for Gradient

impl Debug for Gradient

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.