Struct SecondOrderCone 

pub struct SecondOrderCone<T = f64> { /* private fields */ }

A second-order cone (SOC)

A set of the form

$$ C_{\alpha} = \{x=(y, t) \in \mathbb{R}^{n+1}: t\in\mathbb{R}, \Vert{}y\Vert \leq \alpha{}t\}, $$

where $\alpha$ is a positive scalar.

Projections on the second-order cone are computed as in H.H. Bauschke’s 1996 doctoral dissertation: Projection Algorithms and Monotone Operators (p. 40, Theorem 3.3.6).

Implementations

impl<T: Float> SecondOrderCone<T>

pub fn new(alpha: T) -> SecondOrderCone<T>

Construct a new instance of SecondOrderCone with parameter alpha.

A second-order cone with parameter alpha is the set $C_\alpha = \{x=(y, t) \in \mathbb{R}^{n+1}: t\in\mathbb{R}, \Vert{}y\Vert \leq \alpha t\}$, where $\alpha$ is a positive parameter, and projections are computed according to Theorem 3.3.6 in H.H. Bauschke’s 1996 doctoral dissertation: Projection Algorithms and Monotone Operators (page 40).

Arguments

• alpha: parameter $\alpha$

Panics

The method panics if the given parameter alpha is nonpositive.

Example

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

let cone = SecondOrderCone::new(1.0);
let mut x = [2.0, 0.0, 0.5];
cone.project(&mut x).unwrap();

Trait Implementations

impl<T: Clone> Clone for SecondOrderCone<T>

fn clone(&self) -> SecondOrderCone<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T> Constraint<T> for SecondOrderCone<T>

where T: Float + Sum<T>,

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

Project onto the second-order cone.

Arguments

• x: (in) vector to be projected onto the current second-order cone, (out) its projection onto that cone

Panics

This method panics if the length of x is less than 2.

fn is_convex(&self) -> bool

Returns true if and only if the set is convex

impl<T: Copy> Copy for SecondOrderCone<T>