3.1.1.1. pyprox.douglas_rachford

pyprox.douglas_rachford(prox_f, prox_g, x0, maxiter=1000, mu=1, gamma=1, full_output=0, retall=0, callback=None)

Minimize the sum of two functions using the Douglas Rachford splitting. scheme.

This algorithm assumes that F, G are both “proximable” where the optimization objective reads:

F(x) + G(x)

Parameters :

prox_f : callable

should take two arguments : an ndarray and a float.

prox_g : callable

same as prox_f.

x0 : ndarray

initial guess for the solution.

maxiter : int, optional

maximum number of iterations.

mu : float, optional

gamma : float, optional

full_output : bool, optional

non-zero to return all optional outputs.

retall : bool, optional

Return a list of results at each iteration if non-zero.

callback : callable, optional

An optional user-supplied function to call after each iteration. Called as callback(xk), where xk is the current parameter vector.

Returns :

xrec: ndarray :

fx: list :

References

Proximal Splitting Methods in Signal Processing, Patrick L. Combettes and Jean-Christophe Pesquet, in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, New York: Springer-Verlag, 2010.