atoms.mixed_lasso¶

Module: `atoms.mixed_lasso`¶

Inheritance diagram for regreg.atoms.mixed_lasso:

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Classes¶

`mixed_lasso`¶

class regreg.atoms.mixed_lasso.mixed_lasso(penalty_structure, lagrange, weights={}, offset=None, quadratic=None, initial=None)¶

Bases: regreg.atoms.atom

__init__(penalty_structure, lagrange, weights={}, offset=None, quadratic=None, initial=None)¶: Initialize self. See help(type(self)) for accurate signature.

apply_offset(x)¶: If self.offset is not None, return x-self.offset, else return x.

property conjugate¶: The conjugate of an atom.

constraint(x, bound=None)¶

property dual¶

get_conjugate()¶

get_dual()¶

get_offset()¶

get_quadratic()¶: Get the quadratic part of the composite.

latexify(var=None, idx='')¶

property linear_transform¶

The linear transform applied before a penalty is computed. Defaults to regreg.affine.identity

>>> from regreg.api import l1norm
>>> penalty = l1norm(30, lagrange=3.4)
>>> type(penalty.linear_transform)
<class 'regreg.affine.identity'>

nonsmooth_objective(x, check_feasibility=False)¶

objective(x, check_feasibility=False)¶

objective_template = 'needs a template'¶: A class that defines the API for cone constraints.

objective_vars = {'dualklass': 'dualnorm', 'klass': 'norm', 'offset': '\\alpha', 'shape': 'p', 'var': '\\beta'}¶

property offset¶

proximal(proxq, prox_control=None)¶

The proximal operator. If the atom is in Lagrange mode, this has the form

\[v^{\lambda}(x) = \text{argmin}_{v \in \mathbb{R}^p} \frac{L}{2} \|x-v\|^2_2 + \lambda h(v+\alpha) + \langle v, \eta \rangle\]

where \(\alpha\) is the offset of self.affine_transform and \(\eta\) is self.linear_term.

\[v^{\lambda}(x) = \text{argmin}_{v \in \mathbb{R}^p} \frac{L}{2} \|x-v\|^2_2 + \langle v, \eta \rangle \text{s.t.} \ h(v+\alpha) \leq \lambda\]

proximal_optimum(quadratic)¶

proximal_step(quadratic, prox_control=None)¶

Compute the proximal optimization

Parameters: prox_control: [None, dict]

If not None, then a dictionary of parameters for the prox procedure

property quadratic¶: Quadratic part of the object, instance of regreg.identity_quadratic.identity_quadratic.

seminorm(x, check_feasibility=False)¶

set_offset(value)¶

set_quadratic(quadratic)¶: Set the quadratic part of the composite.

smooth_objective(x, mode='both', check_feasibility=False)¶: The zero function.

smoothed(smoothing_quadratic)¶: Add quadratic smoothing term

solve(quadratic=None, return_optimum=False, **fit_args)¶

tol = 1e-05¶

`mixed_lasso_dual`¶

class regreg.atoms.mixed_lasso.mixed_lasso_dual(penalty_structure, bound, weights={}, offset=None, quadratic=None, initial=None)¶

Bases: regreg.atoms.mixed_lasso.mixed_lasso

__init__(penalty_structure, bound, weights={}, offset=None, quadratic=None, initial=None)¶: Initialize self. See help(type(self)) for accurate signature.

apply_offset(x)¶: If self.offset is not None, return x-self.offset, else return x.

property conjugate¶: The conjugate of an atom.

constraint(x, bound=None)¶

Verify \(\cdot needs a template \leq \lambda\), where \(\lambda\) is bound, \(\alpha\) is self.offset (if any).

If True, returns 0, else returns np.inf.

The class atom’s constraint just returns the appropriate bound parameter for use by the subclasses.

property dual¶

get_conjugate()¶

get_dual()¶

get_offset()¶

get_quadratic()¶: Get the quadratic part of the composite.

latexify(var=None, idx='')¶