Struct ADMMSolver 

pub struct ADMMSolver {
    pub rho: f64,
    pub max_iter: usize,
    pub tol: f64,
}

ADMM solver for problems of the form: min f(x) + g(z) s.t. Ax + Bz = c.

Fields

rho: f64

Penalty parameter ρ > 0.

max_iter: usize

Maximum iterations.

tol: f64

Tolerance.

Implementations

impl ADMMSolver

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

Create a new ADMM solver.

pub fn lasso_convergence_rate(&self, lambda: f64, _n: usize) -> f64

ADMM for LASSO: min (1/2)||Ax-b||^2 + λ||x||_1. Simplified: returns the number of iterations to convergence estimate.

pub fn dual_update(&self, y: f64, primal_residual: f64) -> f64

Dual update: y_{k+1} = y_k + ρ(Ax_{k+1} + Bz_{k+1} - c). Simplified for scalar: returns updated dual variable.

pub fn stopping_criteria(&self, primal_res: f64, dual_res: f64) -> bool

Stopping criteria: primal and dual residuals. primal: ||Ax + Bz - c||, dual: ||ρA^T B(z - z_old)||.

pub fn convergence_bound_at(&self, k: usize, _initial_gap: f64) -> f64

Convergence bound: ADMM converges at O(1/k) for general convex problems.