AxisAlignedEllipsoidalSet

(class from pyomo.contrib.pyros.uncertainty_sets)

class pyomo.contrib.pyros.uncertainty_sets.AxisAlignedEllipsoidalSet(center, half_lengths)

Bases: UncertaintySet

An axis-aligned ellipsoid.

Parameters:

• center ((N,) array_like) – Center of the ellipsoid.

• half_lengths ((N,) array_like) – Semi-axis lengths of the ellipsoid.

Examples

3D origin-centered unit hypersphere:

>>> from pyomo.contrib.pyros import AxisAlignedEllipsoidalSet
>>> sphere = AxisAlignedEllipsoidalSet(
...     center=[0, 0, 0],
...     half_lengths=[1, 1, 1]
... )
>>> sphere.center
array([0, 0, 0])
>>> sphere.half_lengths
array([1, 1, 1])

__init__(center, half_lengths)

Initialize self (see class docstring).

Methods

__init__(center, half_lengths)	Initialize self (see class docstring).
compute_auxiliary_uncertain_param_vals(point)	Compute auxiliary uncertain parameter values for a given point.
is_bounded(config)	Determine whether the uncertainty set is bounded.
is_nonempty(config)	Return True if the uncertainty set is nonempty, else False.
is_valid(config)	Return True if the uncertainty set is bounded and non-empty, else False.
point_in_set(point)	Determine whether a given point lies in the uncertainty set.
set_as_constraint([uncertain_params, block])	Construct a block of Pyomo constraint(s) defining the uncertainty set on variables representing the uncertain parameters, for use in a two-stage robust optimization problem or subproblem (such as a PyROS separation subproblem).

Attributes

center	Center of the ellipsoid.
dim	Dimension N of the axis-aligned ellipsoidal set.
geometry	Geometry of the axis-aligned ellipsoidal set.
half_lengths	Semi-axis lengths.
parameter_bounds	Bounds in each dimension of the axis-aligned ellipsoidal set.
type	Brief description of the type of the uncertainty set.

Member Documentation

compute_auxiliary_uncertain_param_vals(point, solver=None)

Compute auxiliary uncertain parameter values for a given point. The point need not be in the uncertainty set.

Parameters:

• point ((N,) array-like) – Point of interest.

• solver (Pyomo solver, optional) – If needed, a Pyomo solver with which to compute the auxiliary values.

Returns:

aux_space_pt – Computed auxiliary uncertain parameter values.

Return type:

numpy.ndarray

is_bounded(config)

Determine whether the uncertainty set is bounded.

Parameters:

config (ConfigDict) – PyROS solver configuration.

Returns:

True if the uncertainty set is certified to be bounded, and False otherwise.

Return type:

bool

Notes

This check is carried out by solving a sequence of maximization and minimization problems (in which the objective for each problem is the value of a single uncertain parameter). If any of the optimization models cannot be solved successfully to optimality, then False is returned.

This method is invoked during the validation step of a PyROS solver call.

is_nonempty(config)

Return True if the uncertainty set is nonempty, else False.

is_valid(config)

Return True if the uncertainty set is bounded and non-empty, else False.

point_in_set(point)

Determine whether a given point lies in the uncertainty set.

Parameters:

point ((N,) array-like) – Point (parameter value) of interest.

Returns:

is_in_set – True if the point lies in the uncertainty set, False otherwise.

Return type:

bool

Notes

This method is invoked at the outset of a PyROS solver call to determine whether a user-specified nominal parameter realization lies in the uncertainty set.

set_as_constraint(uncertain_params=None, block=None)

Construct a block of Pyomo constraint(s) defining the uncertainty set on variables representing the uncertain parameters, for use in a two-stage robust optimization problem or subproblem (such as a PyROS separation subproblem).

Parameters:

• uncertain_params (None, Var, or list of Var, optional) – Variable objects representing the (main) uncertain parameters. If None is passed, then new variable objects are constructed.

• block (BlockData or None, optional) – Block on which to declare the constraints and any new variable objects. If None is passed, then a new block is constructed.

Returns:

A collection of the components added or addressed.

Return type:

UncertaintyQuantification

property center

Center of the ellipsoid.

Type:

(N,) numpy.ndarray

property dim

Dimension N of the axis-aligned ellipsoidal set.

Type:

int

property geometry

Geometry of the axis-aligned ellipsoidal set. See the Geometry class documentation.

property half_lengths

Semi-axis lengths.

Type:

(N,) numpy.ndarray

property parameter_bounds

Bounds in each dimension of the axis-aligned ellipsoidal set.

Returns:

List, length N, of 2-tuples. Each tuple specifies the bounds in its corresponding dimension.

Return type:

list of tuples

property type

Brief description of the type of the uncertainty set.

Type:

str