picos.constraints.uncertain¶

Constraint types with an explicit representation of data uncertainty.

Outline¶

Classes¶

`BallUncertainNormConstraint`	An (uncertain) upper bound on a norm with unit ball uncertainty.
`ConicallyUncertainAffineConstraint`	A bound on an affine expression with conic uncertainty.
`MomentAmbiguousExtremumAffineConstraint`	A bound on a moment-ambiguous expected value of a piecewise function.
`MomentAmbiguousSquaredNormConstraint`	A bound on a moment-ambiguous expected value of a squared norm.
`ScenarioUncertainConicConstraint`	Conic constraint with scenario uncertainty.
`WassersteinAmbiguousExtremumAffineConstraint`	A bound on a W_1-ambiguous expected value of a piecewise function.
`WassersteinAmbiguousSquaredNormConstraint`	A bound on a Wasserstein-ambiguous expected value of a squared norm.

Submodules¶

`picos.constraints.uncertain.ucon_ball_norm`	Implements `BallUncertainNormConstraint`.
`picos.constraints.uncertain.ucon_conic_aff`	Implements `ConicallyUncertainAffineConstraint`.
`picos.constraints.uncertain.ucon_mom_pwl`	Implements `MomentAmbiguousExtremumAffineConstraint`.
`picos.constraints.uncertain.ucon_mom_sqnorm`	Implements `MomentAmbiguousSquaredNormConstraint`.
`picos.constraints.uncertain.ucon_scen_conic`	Implements `ScenarioUncertainConicConstraint`.
`picos.constraints.uncertain.ucon_ws_pwl`	Implements `WassersteinAmbiguousExtremumAffineConstraint`.
`picos.constraints.uncertain.ucon_ws_sqnorm`	Implements `WassersteinAmbiguousSquaredNormConstraint`.

Classes¶

BallUncertainNormConstraint¶

class picos.constraints.uncertain.BallUncertainNormConstraint(norm, upper_bound)[source]¶

Bases: picos.constraints.constraint.Constraint

An (uncertain) upper bound on a norm with unit ball uncertainty.

class RobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Robust counterpart conversion.

classmethod convert(con, options)[source]¶

Implement convert.

Conversion recipe and variable names based on the book Robust Optimization (Ben-Tal, El Ghaoui, Nemirovski, 2009).

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(norm, upper_bound)[source]¶

Construct a BallUncertainNormConstraint.

Parameters

norm (UncertainNorm) – Uncertain norm that is bounded from above.
upper_bound (AffineExpression or UncertainAffineExpression) – (Uncertain) upper bound on the norm.

property ne¶: The uncertain affine expression under the norm.

ConicallyUncertainAffineConstraint¶

class picos.constraints.uncertain.ConicallyUncertainAffineConstraint(le0)[source]¶

Bases: picos.constraints.constraint.Constraint

A bound on an affine expression with conic uncertainty.

class RobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Robust counterpart conversion.

classmethod convert(con, options)[source]¶

Implement convert.

Conversion recipe and variable names based on the book Robust Optimization (Ben-Tal, El Ghaoui, Nemirovski, 2009).

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(le0)[source]¶

Construct an ConicallyUncertainAffineConstraint.

Parameters: le0 (UncertainAffineExpression) – Uncertain expression constrained to be at most zero.

MomentAmbiguousExtremumAffineConstraint¶

class picos.constraints.uncertain.MomentAmbiguousExtremumAffineConstraint(extremum, relation, rhs)[source]¶

Bases: picos.constraints.constraint.Constraint

A bound on a moment-ambiguous expected value of a piecewise function.

class DistributionallyRobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Distributionally robust counterpart conversion.

classmethod convert(con, options)[source]¶: Implement convert.

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(extremum, relation, rhs)[source]¶

Construct a MomentAmbiguousExtremumAffineConstraint.

Parameters

extremum (RandomExtremumAffine) – Left hand side expression.
relation (str) – Constraint relation symbol.
rhs (AffineExpression) – Right hand side expression.

property maximum_form¶: The constraint posed as an upper bound on an expected maximum.

MomentAmbiguousSquaredNormConstraint¶

class picos.constraints.uncertain.MomentAmbiguousSquaredNormConstraint(sqnorm, upper_bound)[source]¶

Bases: picos.constraints.constraint.Constraint

A bound on a moment-ambiguous expected value of a squared norm.

class DistributionallyRobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Distributionally robust counterpart conversion.

classmethod convert(con, options)[source]¶: Implement convert.

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(sqnorm, upper_bound)[source]¶

Construct a MomentAmbiguousSquaredNormConstraint.

Parameters

sqnorm (UncertainSquaredNorm) – Uncertain squared norm to upper bound the expectation of.
upper_bound (AffineExpression) – Upper bound on the expected value.

ScenarioUncertainConicConstraint¶

class picos.constraints.uncertain.ScenarioUncertainConicConstraint(element, cone)[source]¶

Bases: picos.constraints.constraint.Constraint

Conic constraint with scenario uncertainty.

class RobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Robust counterpart conversion.

classmethod convert(con, options)[source]¶: Implement convert.

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(element, cone)[source]¶

Construct a ScenarioUncertainConicConstraint.

Parameters

element (UncertainAffineExpression) – Uncertain expression constrained to be in the cone.
cone (Cone) – The cone that the uncertain expression is constrained to.

WassersteinAmbiguousExtremumAffineConstraint¶

class picos.constraints.uncertain.WassersteinAmbiguousExtremumAffineConstraint(extremum, relation, rhs)[source]¶

Bases: picos.constraints.constraint.Constraint

A bound on a W_1-ambiguous expected value of a piecewise function.

class DistributionallyRobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Distributionally robust counterpart conversion.

classmethod convert(con, options)[source]¶: Implement convert.

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(extremum, relation, rhs)[source]¶

Construct a WassersteinAmbiguousExtremumAffineConstraint.

Parameters

extremum (RandomExtremumAffine) – Left hand side expression.
relation (str) – Constraint relation symbol.
rhs (AffineExpression) – Right hand side expression.

property maximum_form¶: The constraint posed as an upper bound on an expected maximum.

WassersteinAmbiguousSquaredNormConstraint¶

class picos.constraints.uncertain.WassersteinAmbiguousSquaredNormConstraint(sqnorm, upper_bound)[source]¶

Bases: picos.constraints.constraint.Constraint

A bound on a Wasserstein-ambiguous expected value of a squared norm.

class DistributionallyRobustConversion[source]¶

Bases: picos.constraints.constraint.ConstraintConversion

Distributionally robust counterpart conversion.

classmethod convert(con, options)[source]¶: Implement convert.

classmethod predict(subtype, options)[source]¶: Implement predict.

__init__(sqnorm, upper_bound)[source]¶

Construct a WassersteinAmbiguousSquaredNormConstraint.

Parameters

sqnorm (UncertainSquaredNorm) – Uncertain squared norm to upper bound the expectation of.
upper_bound (AffineExpression) – Upper bound on the expected value.