def METHOD_NAME(r, t, x, g, v, norm_coefficient, alpha, beta):  # type: ignore
    # Add gradient of regularization term.
    g_regularized = norm_coefficient * x + g
    # Coefficient of gradient should be 1 at the first iteration.
    beta_adjusted = beta if t > 0 else 1
    # Update momentum.
    v_new = alpha * v + beta_adjusted * g_regularized
    # Apply SG with momentum update rule.
    x_new = x - r * v_new
    return x_new, v_new