picos.expressions.exp_extremum

Implements MaximumConvex and MinimumConcave.

Outline

Classes

Extremum	Base class for MaximumConvex and MinimumConcave.
ExtremumBase	Base class for Extremum and similar classes.
MaximumBase	Base implementation of ExtremumBase for maximums.
MaximumConvex	The maximum over a set of convex scalar expressions.
MinimumBase	Base implementation of ExtremumBase for minimums.
MinimumConcave	The minimum over a set of concave scalar expressions.

Classes

Extremum

class picos.expressions.exp_extremum.Extremum(expressions)

Bases: picos.expressions.exp_extremum.ExtremumBase, picos.expressions.expression.Expression

Base class for MaximumConvex and MinimumConcave.

Note

This can represent the maximum (minimum) over convex (concave) uncertain expressions as long as the uncertainty is not of stochastic nature. In this case, the extremum implicitly goes over the perturbation parameters as well.

__init__(expressions)

Construct a MaximumConvex or MinimumConcave.

Parameters

expressions – A collection of all convex or all concave expressions.

property expressions

The expressions under the extremum.

ExtremumBase

class picos.expressions.exp_extremum.ExtremumBase

Bases: abc.ABC

Base class for Extremum and similar classes.

In particular, this is also used by the uncertain RandomExtremumAffine.

Must be inherited with priority with respect to Expression.

property argnum

Number of expressions under the extremum.

abstract property expressions

The expressions under the extremum.

MaximumBase

class picos.expressions.exp_extremum.MaximumBase

Bases: object

Base implementation of ExtremumBase for maximums.

MaximumConvex

class picos.expressions.exp_extremum.MaximumConvex(expressions)

Bases: picos.expressions.exp_extremum.MaximumBase, picos.expressions.exp_extremum.Extremum

The maximum over a set of convex scalar expressions.

Example

>>> import picos
>>> x = picos.RealVariable("x", 4)
>>> a = abs(x)
>>> b = picos.sum(x)
>>> c = picos.max([a, b]); c
<Maximum of Convex Functions: max(‖x‖, ∑(x))>
>>> 2*c
<Scaled Maximum of Convex Functions: 2·max(‖x‖, ∑(x))>
>>> c <= 5
<Maximum of Convex Functions Constraint: max(‖x‖, ∑(x)) ≤ 5>

MinimumBase

class picos.expressions.exp_extremum.MinimumBase

Bases: object

Base implementation of ExtremumBase for minimums.

MinimumConcave

class picos.expressions.exp_extremum.MinimumConcave(expressions)

Bases: picos.expressions.exp_extremum.MinimumBase, picos.expressions.exp_extremum.Extremum

The minimum over a set of concave scalar expressions.

Example

>>> import picos
>>> x = picos.RealVariable("x", 4)
>>> a = picos.sum(x)
>>> b = 2*a
>>> c = picos.min([a, b]); c
<Minimum of Concave Functions: min(∑(x), 2·∑(x))>
>>> -1*c
<Maximum of Convex Functions: max(-∑(x), -2·∑(x))>
>>> C = 5 <= c; C
<Minimum of Concave Functions Constraint: min(∑(x), 2·∑(x)) ≥ 5>
>>> x.value = 1
>>> C.slack
-1.0