gdprox, proximal gradient-descent algorithms

Implements the proximal gradient-descent algorithm for composite objective functions, i.e. functions of the form f(x) + g(x), where f is a smooth function and g is a possibly non-smooth function for which the proximal operator is known.

The main function in this package is gdprox.fmin_cgprox. This function follows a similar interface than the functions in scipy.optimize. The definition of this function is:

def fmin_cgprox(f, fprime, g_prox, x0, rtol=1e-6,
                maxiter=1000, verbose=0, default_step_size=1.):
    """
    proximal gradient-descent solver for optimization problems of the form

                       minimize_x f(x) + g(x)

    where f is a smooth function and g is a (possibly non-smooth)
    function for which the proximal operator is known.

    Parameters
    ----------
    f : callable
        f(x) returns the value of f at x.

    f_prime : callable
        f_prime(x) returns the gradient of f.

    g_prox : callable of the form g_prox(x, alpha)
        g_prox(x, alpha) returns the proximal operator of g at x
        with parameter alpha.

    x0 : array-like
        Initial guess

    maxiter : int
        Maximum number of iterations.

    verbose : int
        Verbosity level, from 0 (no output) to 2 (output on each iteration)

    default_step_size : float
        Starting value for the line-search procedure.

    Returns
    -------
    res : OptimizeResult
        The optimization result represented as a
        ``scipy.optimize.OptimizeResult`` object. Important attributes are:
        ``x`` the solution array, ``success`` a Boolean flag indicating if
        the optimizer exited successfully and ``message`` which describes
        the cause of the termination. See `scipy.optimize.OptimizeResult`
        for a description of other attributes.
    """