pyproximal.optimization.primal.ProximalGradient¶

pyproximal.optimization.primal.ProximalGradient(proxf: ProxOperator, proxg: ProxOperator, x0: ndarray[tuple[Any, ...], dtype[_ScalarT]], epsg: float | ndarray[tuple[Any, ...], dtype[_ScalarT]] = 1.0, tau: float | None = None, backtracking: bool = False, beta: float = 0.5, eta: float = 1.0, niter: int = 10, niterback: int = 100, acceleration: str | None = None, 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]][source]¶

Proximal gradient (optionally accelerated)

Solves the following minimization problem using (Accelerated) Proximal gradient algorithm:

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

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 \(\nabla f\). When tau=None, backtracking is used to adaptively estimate the best tau at each iteration. Finally, note that \(\tau\) can be chosen to be a vector when dealing with problems with multiple right-hand-sides
backtrackingbool, optional: Force backtracking, even if tau is not equal to None. In this case the chosen tau will be used as the initial guess in the first step of backtracking
betafloat, optional: Backtracking parameter (must be between 0 and 1)
etafloat, optional: Relaxation parameter (must be between 0 and 1, 0 excluded).
niterint, optional: Number of iterations of iterative scheme
niterbackint, optional: Max number of iterations of backtracking
accelerationstr, optional: Acceleration (None, vandenberghe or fista)
tolfloat, optional: Tolerance on change of objective function (used as stopping criterion). If tol=None, run until niter is reached or the other tolerance criterion is met
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: