def METHOD_NAME(dim):
    """
    Creade the cvxpy ``Problem`` for the dnorm metric using dense arrays
    """
    X, constraints = initialize_constraints_on_dnorm_problem(dim)
    Jr = cvxpy.Parameter((dim**2, dim**2))
    Ji = cvxpy.Parameter((dim**2, dim**2))
    # The objective, however, depends on J.
    objective = cvxpy.Maximize(cvxpy.trace(Jr.T @ X.re + Ji.T @ X.im))
    problem = cvxpy.Problem(objective, constraints)
    return problem, Jr, Ji