Struct Halfspace 

pub struct Halfspace<'a, T = f64> { /* private fields */ }

A halfspace is a set given by $H = \{x \in \mathbb{R}^n {}:{} \langle c, x\rangle \leq b\}$.

Implementations

impl<'a, T> Halfspace<'a, T>

where T: Float + Sum<T>,

pub fn new(normal_vector: &'a [T], offset: T) -> Self

A halfspace is a set given by $H = \{x \in \mathbb{R}^n {}:{} \langle c, x\rangle \leq b\}$, where $c$ is the normal vector of the halfspace and $b$ is an offset.

This method constructs a new instance of Halfspace with a given normal vector and bias

Arguments

• normal_vector: the normal vector, $c$, as a slice
• offset: the offset parameter, $b$

Returns

New instance of Halfspace

Panics

Does not panic. Note: it does not panic if you provide an empty slice as normal_vector, but you should avoid doing that.

Example

use optimization_engine::constraints::{Constraint, Halfspace};

let normal_vector = [1., 2.];
let offset = 1.0;
let halfspace = Halfspace::new(&normal_vector, offset);
let mut x = [-1., 3.];
halfspace.project(&mut x).unwrap();

Trait Implementations

impl<'a, T: Clone> Clone for Halfspace<'a, T>

fn clone(&self) -> Halfspace<'a, T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<'a, T> Constraint<T> for Halfspace<'a, T>

where T: Float + Sum<T>,

fn project(&self, x: &mut [T]) -> FunctionCallResult

Projects on halfspace using the following formula:

$$\begin{aligned} \mathrm{proj}_{H}(x) = \begin{cases} x,& \text{ if } \langle c, x\rangle \leq b \\ x - \frac{\langle c, x\rangle - b} {\|c\|}c,& \text{else} \end{cases} \end{aligned}$$

where $H = \{x \in \mathbb{R}^n {}:{} \langle c, x\rangle \leq b\}$

Arguments

• x: (in) vector to be projected on the current instance of a halfspace, (out) projection on the second-order cone

Panics

This method panics if the length of x is not equal to the dimension of the halfspace.

fn is_convex(&self) -> bool

Halfspaces are convex sets

Returns

Returns true