pyproximal.L0

class pyproximal.L0(sigma: float | ndarray[tuple[Any, ...], dtype[_ScalarT]] | Callable[[int], float | ndarray[tuple[Any, ...], dtype[_ScalarT]]] = 1.0)

\(L_0\) norm proximal operator.

Proximal operator of the \(\ell_0\) norm: \(\sigma\|\mathbf{x}\|_0 = \text{count}(x_i \ne 0)\).

Parameters:

sigmafloat or numpy.ndarray or func, optional

Multiplicative coefficient of L0 norm. This can be a constant number, a list of values (for multidimensional inputs, acting on the second dimension) or a function that is called passing a counter which keeps track of how many times the prox method has been invoked before and returns a scalar (or a list of) sigma to be used.

Notes

The \(\ell_0\) proximal operator is defined as:

\[\begin{split}\prox_{\tau \sigma \|\cdot\|_0}(\mathbf{x}) = \operatorname{hard}(\mathbf{x}, \tau \sigma) = \begin{cases} x_i, & x_i < -\tau \sigma \\ 0, & -\tau\sigma \leq x_i \leq \tau\sigma \\ x_i, & x_i > \tau\sigma\\ \end{cases}\end{split}\]

where \(\operatorname{hard}\) is the so-called called hard thresholding.

Methods

__init__([sigma])
affine_addition(v)	Affine addition
chain(g)	Chain
grad(x)	Gradient of the Moreau envelope of the function.
postcomposition(sigma)	Postcomposition
precomposition(a, b)	Precomposition
prox(*args, **kwargs)
proxdual(**kwargs)

Examples using pyproximal.L0

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