<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def dca(x, f, g, niter, callback=None):
 r"""Subgradient DCA of Tao and An. This algorithm solves a problem of the form :: min_x f(x) - g(x), where ``f`` and ``g`` are proper, convex and lower semicontinuous functions. Parameters x : `LinearSpaceElement` Initial point, updated in-place. f : `Functional` Convex functional. Needs to implement ``f.convex_conj.gradient``. g : `Functional` Convex functional. Needs to implement ``g.gradient``. niter : int Number of iterations. callback : callable, optional Function called with the current iterate after each iteration. Notes ----- The algorithm is described in Section 3 and in particular in Theorem 3 of `[TA1997] <http://journals.math.ac.vn/acta/pdf/9701289.pdf>`_. The problem .. math:: \min f(x) - g(x) has the first-order optimality condition :math:`0 \in \partial f(x) - \partial g(x)`, i.e., aims at finding an :math:`x` so that there exists a common element .. math:: y \in \partial f(x) \cap \partial g(x). The element :math:`y` can be seen as a solution of the Toland dual problem .. math:: \min g^*(y) - f^*(y) and the iteration is given by .. math:: y_n \in \partial g(x_n), \qquad x_{n+1} \in \partial f^*(y_n), for :math:`n\geq 0`. Here, a subgradient is found by evaluating the gradient method of the respective functionals. References [TA1997] Tao, P D, and An, L T H. *Convex analysis approach to d.c. programming: Theory, algorithms and applications*. Acta Mathematica Vietnamica, 22.1 (1997), pp 289--355. See also -------- prox_dca : Solver with a proximal step for ``f`` and a subgradient step for ``g``. doubleprox_dc : Solver with proximal steps for all the nonsmooth convex functionals and a gradient step for a smooth functional. """

    space = f.domain
    if g.domain != space:
        raise ValueError('`f.domain` and `g.domain` need to be equal, but '
                         '{} != {}'.format(space, g.domain))
    f_convex_conj = f.convex_conj
    for _ in range(niter):
        f_convex_conj.gradient(g.gradient(x), out=x)

        if callback is not None:
            callback(x)