pyproximal.optimization.primal.AndersonProximalGradient

pyproximal.optimization.primal.AndersonProximalGradient(proxf: ProxOperator, proxg: ProxOperator, x0: ndarray[tuple[Any, ...], dtype[_ScalarT]], epsg: float | ndarray[tuple[Any, ...], dtype[_ScalarT]] = 1.0, tau: float | ndarray[tuple[Any, ...], dtype[_ScalarT]] = 1.0, niter: int = 10, nhistory: int = 10, epsr: float = 1e-10, safeguard: bool = False, tol: float | None = None, rtol: float | None = None, callback: Callable[[ndarray[tuple[Any, ...], dtype[_ScalarT]]], None] | None = None, show: bool = False, itershow: tuple[int, int, int] = (10, 10, 10)) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

Proximal gradient with Anderson acceleration

Solves the following minimization problem using the Proximal gradient algorithm with Anderson acceleration:

\[\mathbf{x} = \argmin_\mathbf{x} f(\mathbf{x}) + \epsilon g(\mathbf{x})\]

where \(f(\mathbf{x})\) is a smooth convex function with a uniquely defined gradient and \(g(\mathbf{x})\) is any convex function that has a known proximal operator.

Parameters:

proxfpyproximal.ProxOperator

Proximal operator of f function (must have grad implemented)

proxgpyproximal.ProxOperator

Proximal operator of g function

x0numpy.ndarray

Initial vector

epsgfloat or numpy.ndarray, optional

Scaling factor of g function. Can be a scalar for iteration-independent scaling or a a 1d vector for iteration-dependent scaling

taufloat or numpy.ndarray, optional

Positive scalar weight, which should satisfy the following condition to guarantees convergence: \(\tau \in (0, 1/L]\) where L is the Lipschitz constant of \(\nabla f\). N ote that \(\tau\) can be chosen to be a vector when dealing with problems with multiple right-hand-sides

niterint, optional

Number of iterations of iterative scheme

nhistoryint, optional

Number of previous iterates to be kept in memory (to compute the scaling factors

epsrfloat, optional

Scaling factor for regularization added to the inverse of :math:mathbf{R}^T mathbf{R}`

safeguardbool, optional

Apply safeguarding strategy to the update (True) or not (False)

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

Notes

See pyproximal.optimization.cls_primal.AndersonProximalGradient

Examples using pyproximal.optimization.primal.AndersonProximalGradient

IHT, ISTA, FISTA, AA-ISTA, and TWIST for Compressive sensing

IHT, ISTA, FISTA, AA-ISTA, and TWIST for Compressive sensing