pyproximal.optimization.primal.PPXA¶

pyproximal.optimization.primal.PPXA(proxfs: list[ProxOperator], x0: ndarray[tuple[Any, ...], dtype[_ScalarT]] | list[ndarray[tuple[Any, ...], dtype[_ScalarT]]], tau: float, eta: float = 1.0, weights: ndarray[tuple[Any, ...], dtype[_ScalarT]] | list[float] | None = None, niter: int = 1000, tol: float | None = None, rtol: float | None = None, callback: Callable[[...], None] | None = None, show: bool = False, itershow: tuple[int, int, int] = (10, 10, 10)) → ndarray[tuple[Any, ...], dtype[_ScalarT]][source]¶

Parallel Proximal Algorithm (PPXA)

Solves the following minimization problem using Parallel Proximal Algorithm (PPXA):

\[\mathbf{x} = \argmin_\mathbf{x} \sum_{i=1}^m f_i(\mathbf{x})\]

where \(f_i(\mathbf{x})\) are any convex functions that has known proximal operators.

Parameters:

proxfslist: A list of proximable functions \(f_1, \ldots, f_m\).
x0numpy.ndarray or list: Initial vector \(\mathbf{x}\) for all \(f_i\) if 1-dimensional array is provided, or initial vectors \(\mathbf{x}_{i}\) for each \(f_i\) for \(i=1,\ldots,m\) if a list of 1-dimensional arrays or a 2-dimensional array of size (m, d) is provided, where d is the dimension of \(\mathbf{x}_{i}\).
taufloat: Positive scalar weight
etafloat, optional: Relaxation parameter (must be between 0 and 2, 0 excluded).
weightsnumpy.ndarray or list or None, optional: Weights \(\sum_{i=1}^m w_i = 1, \ 0 < w_i < 1\), Defaults to None, which means \(w_1 = \cdots = w_m = \frac{1}{m}.\)
niterint, optional: Number of iterations of iterative scheme.
tolfloat, optional: Tolerance on change of objective function (used as stopping criterion). If tol=None, run until niter is reached
rtolfloat, optional: Relative tolerance on objective function wrt initial value. Stops the solver when the ratio of the current objective function to the initial objective function is below this value. If rtol=None, run until niter is reached or the other tolerance criterion is met
callbackcallable, optional: Function with signature (callback(x)) to call after each iteration where x is the current model vector
showbool, optional: Display iterations log
itershowtuple, optional: Display set log for the first N1 steps, last N2 steps, and every N3 steps in between where N1, N2, N3 are the three element of the list.

Returns:

xnumpy.ndarray: Inverted model