Struct DualDecomposition 

pub struct DualDecomposition {
    pub step_size: f64,
    pub max_iter: usize,
    pub tol: f64,
}

Lagrangian relaxation with subgradient updates for dual decomposition.

Minimises f(x) + g(z) subject to Ax + Bz = c by relaxing the coupling constraint. The dual variables y are updated using the subgradient of the dual function.

Fields

step_size: f64

Step size for dual variable updates.

max_iter: usize

Maximum number of dual iterations.

tol: f64

Convergence tolerance on the primal feasibility gap ‖Ax + Bz − c‖.

Implementations

impl DualDecomposition

pub fn new(step_size: f64, max_iter: usize, tol: f64) -> Self

Create a new DualDecomposition solver.

pub fn solve( &self, x_init: Vec<f64>, z_init: Vec<f64>, y_init: Vec<f64>, x_solve: &dyn Fn(&[f64], &[f64]) -> Vec<f64>, z_solve: &dyn Fn(&[f64], &[f64]) -> Vec<f64>, mat_a: &[Vec<f64>], mat_b: &[Vec<f64>], c: &[f64], ) -> (Vec<f64>, Vec<f64>, Vec<f64>, usize)

Run dual decomposition.

• x_solve: minimiser of the Lagrangian w.r.t. x given dual y and z.
• z_solve: minimiser of the Lagrangian w.r.t. z given dual y and x.
• mat_a, mat_b, c: constraint Ax + Bz = c.

Returns (x_best, z_best, y_final, iterations).