copt.penalty.L1Norm

class copt.penalty.L1Norm(alpha)

L1 norm, that is, the sum of absolute values:

\[\alpha\sum_i^d |x_i|\]

Args: alpha: float

constant multiplying the L1 norm

__init__(alpha)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(alpha)	Initialize self.
prox(x, step_size)	Proximal operator of the L1 norm.
prox_factory(n_features)	Proximal operator of the L1 norm.

prox(x, step_size)

Proximal operator of the L1 norm.

This routine can be used in gradient-based methods like minimize_proximal_gradient, minimize_three_split and minimize_primal_dual.

prox_factory(n_features)

Proximal operator of the L1 norm.

This method is meant to be used with stochastic algorithms that need access to a proximal operator over a potentially sparse vector, like minimize_saga, minimize_svrg and minimize_vrtos