picos.expressions.uncertain.perturbation

Implements a parameterization for (random) noise in data.

Outline

Classes

Perturbation	A parameter that can be used to describe (random) noise in data.
PerturbationUniverse	Base class for uncertain perturbation sets and distributions.
PerturbationUniverseType	Container for a pair of perturbation universe class type and subtype.

Classes

Perturbation

class picos.expressions.uncertain.perturbation.Perturbation(universe, name, shape)

Bases: picos.expressions.mutable.Mutable, picos.expressions.uncertain.uexp_affine.UncertainAffineExpression

A parameter that can be used to describe (random) noise in data.

This is the initial building block for an UncertainAffineExpression. In particular, an affine transformation of this parameter represents uncertain data.

__init__(universe, name, shape)

Create a Perturbation.

Parameters

• universe (PerturbationUniverse) – Either the set that the perturbation parameter lives in or the distribution according to which the perturbation is distributed.

• name (str) – Symbolic string description of the perturbation, similar to a variable’s name.

• shape (int or tuple or list) – Algebraic shape of the perturbation parameter.

This constructor is meant for internal use. As a user, you will want to first define a universe (e.g. ConicPerturbationSet) for the parameter and obtain the parameter from it.

copy(new_name=None)

Return an independent copy of the perturbation.

property universe

The uncertainty universe that the parameter belongs to.

PerturbationUniverse

class picos.expressions.uncertain.perturbation.PerturbationUniverse

Bases: abc.ABC

Base class for uncertain perturbation sets and distributions.

See distributional for a distinction between perturbation sets, random distributions and distributional ambiguity sets, all three of which can be represented by this class.

The naming scheme for implementing classes is as follows:

• Perturbation sets (robust optimization) end in PerturbationSet,

• random distributions (stochastic programming) end in Distribution,

• distributional ambiguity sets (DRO) end in AmbiguitySet.

classmethod make_type(*args, **kwargs)

Create a detailed universe type from subtype parameters.

worst_case(scalar, direction)

Find a worst-case realization of the uncertainty for an expression.

Parameters

• scalar (UncertainExpression) – A scalar uncertain expression that depends only on the perturbation parameter.

• direction (str) – Either "min" or "max", denoting the worst-case direction.

Returns

A pair where the first element is the worst-case (expeceted) value as a float and where the second element is a realization of the perturbation parameter that attains this worst case as a float or CVXOPT matrix (or None for stochastic uncertainty).

Raises

• TypeError – When the function is not scalar.

• ValueError – When the function depends on other mutables than exactly the parameter.

• picos.uncertain.IntractableWorstCase – When computing the worst-case (expected) value is not supported, in particular when it would require solving a nonconvex problem.

• RuntimeError – When the computation is supported but fails.

abstract property distributional

Whether this is a distribution or distributional ambiguity set.

If this is True, then this represents a random distribution (stochastic programming) or an ambiguity set of random distributions (distributionally robust optimization) and any expression that depends on its random parameter, when used in a constraint or as an objective function, is understood as a (worst-case) expected value.

If this is False, then this represents a perturbation set (robust optimization) and any expression that depends on its perturbation parameter, when used in a constraint or as an objective function, is understood as a worst-case value.

abstract property parameter

The perturbation parameter.

property subtype

property type

Detailed type of a perturbation parameter universe.

PerturbationUniverseType

class picos.expressions.uncertain.perturbation.PerturbationUniverseType(theClass, subtype)

Bases: picos.containers.DetailedType

Container for a pair of perturbation universe class type and subtype.