"""ADMM-lite node stub.

This file contains a very small ADMM-like iterative collaborator that exchanges
dual updates and tries to improve a local objective. The real system would
use network transport and privacy-preserving aggregation; this stub focuses on
the local update loop and simple utility computation for tests.
"""
from typing import Any, Dict
from dataclasses import dataclass, field


@dataclass
class ADMMNode:
    node_id: str
    local_x: float = 0.0
    dual: float = 0.0
    rho: float = 1.0

    def local_objective(self, x: float) -> float:
        # simple quadratic objective with a local preferred point
        preferred = 10.0
        return (x - preferred) ** 2

    def step(self, global_avg: float) -> float:
        # ADMM-style proximal step: minimize 0.5*(x - preferred)^2 + (rho/2)*(x - z + u)^2
        # here we do a single closed-form proximal update for a quadratic
        preferred = 10.0
        z = global_avg
        u = self.dual
        # minimize (x-pref)^2 + rho*(x - z + u)^2
        denom = 1.0 + self.rho
        num = 2 * preferred + 2 * self.rho * (z - u)
        x_new = num / (2 * denom)
        self.local_x = x_new
        # update dual as simple gradient step
        self.dual = u + (x_new - z)
        return x_new