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. This package relies on numpy and scipy. scikit-learn is also required to run the test suite.
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.
"""