Struct optimization_engine::constraints::BallInf

pub struct BallInf<'a> { /* fields omitted */ }

An infinity ball defined as $B_\infty^r = \{x\in\mathbb{R}^n {}:{} \Vert{}x{}\Vert_{\infty} \leq r\}$, where $\Vert{}\cdot{}\Vert_{\infty}$ is the infinity norm. The infinity ball centered at a point $x_c$ is defined as $B_\infty^{x_c,r} = \{x\in\mathbb{R}^n {}:{} \Vert{}x-x_c{}\Vert_{\infty} \leq r\}$.

Implementations

impl<'a> BallInf<'a>

pub fn new(center: Option<&'a [f64]>, radius: f64) -> Self

Construct a new infinity-norm ball with given center and radius If no center is given, then it is assumed to be in the origin

Trait Implementations

impl<'a> Clone for BallInf<'a>

fn clone(&self) -> BallInf<'a>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a> Constraint for BallInf<'a>

fn project(&self, x: &mut [f64])

Computes the projection of a given vector x on the current infinity ball.

The projection of a $v\in\mathbb{R}^{n}$ on $B_\infty^r$ is given by $\Pi_{B_\infty^r}(v) = z$ with

$$ z_i = \begin{cases}v_i,&\text{ if } |z_i| \leq r\\\mathrm{sng}(v_i)r,&\text{ otherwise}\end{cases} $$

for all $i=1,\ldots, n$, where sgn is the sign function.

The projection of $v\in\mathbb{R}^{n}$ on $B_\infty^{x_c,r}$ is given by $\Pi_{B_\infty^r}(v) = z$ with

$$ z_i = \begin{cases}v_i,&\text{ if } |z_i-x_{c, i}| \leq r\\x_{c,i} + \mathrm{sng}(v_i)r,&\text{ otherwise}\end{cases} $$

for all $i=1,\ldots, n$.

fn is_convex(&self) -> bool

Returns true if and only if the set is convex

impl<'a> Copy for BallInf<'a>