Function csp_lagrangian 

pub fn csp_lagrangian(
    from: &[usize],
    to: &[usize],
    w_cost: &[f64],
    w_res: &[f64],
    n_nodes: usize,
    source: usize,
    target: usize,
    budget: f64,
    max_iter: usize,
) -> Option<LagrangianRoute>

Constrained shortest path by Lagrangian relaxation (the LARAC algorithm): minimize cost subject to resource <= budget, dualizing the constraint so each iteration is a plain Dijkstra on cost + lambda * resource. A binary search on the two support paths (cheapest-infeasible and feasible-so-far) drives lambda to the maximizer of the dual, which takes few iterations and scales to graphs where exact label-setting is slow.

Returns the best feasible path found with the best dual lower bound on the optimal cost: when cost == lower_bound the path is provably optimal; otherwise it is feasible and within cost - lower_bound of the optimum (the duality gap — close it with pareto_paths, which is exact). Returns None when the target is unreachable or no path fits the budget.