LinearProblem¶

class LinearProblem(*args)¶

Linear optimization problem.

This defines a linear problem as:

$\min_{\vect{x} \in B} f(\vect{x}) = \vect{c}^T \vect{x} \\ \vect{lc_l} \leq \mat{A} \vect{x} \leq \vect{lc_u}$

where $B$ are the problem bounds, $\vect{c}$ is the cost vector, $\mat{A}$ is the constraint matrix term, and $\vect{cb_l}, \vect{cb_u}$ are the constraints bounds terms.

Parameters:

costFunction: The cost vector $\vect{c}$ .
boundsInterval: Bound constraints $B$
AMatrix: Linear inequality constraints matrix $\mat{A}$
cbInterval: Linear inequality constraints bounds terms $\vect{cb_l}, \vect{cb_u}$

Methods

`Linearize`(problem, location)	Transform a general optimization problem to a linear problem.
`getBounds`()	Accessor to bounds.
`getClassName`()	Accessor to the object's name.
`getDimension`()	Accessor to input dimension.
`getEqualityConstraint`()	Accessor to equality constraints.
`getInequalityConstraint`()	Accessor to inequality constraints.
`getLevelFunction`()	Accessor to level function.
`getLevelValue`()	Accessor to level value.
`getLinearConstraintBounds`()	Accessor to the linear constraint bounds.
`getLinearConstraintCoefficients`()	Accessor to the linear constraint term.
`getLinearCost`()	Accessor to the linear cost.
`getName`()	Accessor to the object's name.
`getObjective`()	Accessor to objective function.
`getResidualFunction`()	Accessor to level function.
`getVariablesType`()	Accessor to the variables type.
`hasBounds`()	Test whether bounds had been specified.
`hasEqualityConstraint`()	Test whether equality constraints had been specified.
`hasInequalityConstraint`()	Test whether inequality constraints had been specified.
`hasLevelFunction`()	Test whether level function had been specified.
`hasMultipleObjective`()	Test whether objective function is a scalar or vector function.
`hasName`()	Test if the object is named.
`hasResidualFunction`()	Test whether a least-square problem is defined.
`isContinuous`()	Check if the problem is continuous.
`isLinear`()	Check if the problem is linear.
`isMinimization`([marginalIndex])	Test whether this is a minimization or maximization problem.
`setBounds`(bounds)	Accessor to bounds.
`setEqualityConstraint`(equalityConstraint)	Accessor to equality constraints.
`setInequalityConstraint`(inequalityConstraint)	Accessor to inequality constraints.
`setLevelFunction`(levelFunction)	Accessor to level function.
`setLevelValue`(levelValue)	Accessor to level value.
`setLinearConstraint`(constraintCoefficients, LU)	Accessor to the linear constraint term.
`setLinearCost`(cost)	Accessor to the linear cost.
`setMinimization`(minimization[, marginalIndex])	Tell whether this is a minimization or maximization problem.
`setName`(name)	Accessor to the object's name.
`setObjective`(objective)	Accessor to objective function.
`setResidualFunction`(residualFunction)	Accessor to level function.
`setVariablesType`(variableType)	Accessor to the variables type.

Examples

Define a mixed integer linear optimization problem with objective:

$f = 1.1 x_0 + x_1, x_0 \in \Zset, x_1 \in \Rset$

with inequality constraints:

$\begin{eqnarray*} & x_1 & \leq 7\\ 5 & \leq x_0 + 2x_1 & \leq 15\\ 6 & \leq 3x_0 + 2x_1 & \\ \end{eqnarray*}$

and bound constraints:

$\begin{eqnarray*} 0 & \leq x_0 & \leq 4\\ 1 & \leq x_1 & \end{eqnarray*}$

>>> import openturns as ot
>>> import openturns.experimental as otexp
>>> cost = [1.1, 1.0]
>>> bounds = ot.Interval([0.0, 1.0], [4.0, 1e30])
>>> A = ot.Matrix([[0.0, 1.0], [1.0, 2.0], [3.0, 2.0]])
>>> lcb = ot.Interval([-1e9, 5.0, 6.0], [7.0, 15.0, 1e9])
>>> problem = otexp.LinearProblem(cost, bounds, A, lcb)
>>> problem.setVariablesType([ot.OptimizationProblemImplementation.INTEGER, ot.OptimizationProblemImplementation.CONTINUOUS])

__init__(*args)¶

static Linearize(problem, location)¶

Transform a general optimization problem to a linear problem.

Objective and inequality constraints coefficients are computed from their gradients at the specified location.

Parameters:

problemOptimizationProblem: The problem to linearize
locationsequence of float: The linearization location

Returns:

linearProblemLinearProblem: The linear problem

getBounds()¶

Accessor to bounds.

Returns:

boundsInterval: Problem bounds.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getDimension()¶

Accessor to input dimension.

Returns:

dimensionint: Input dimension of objective function.

getEqualityConstraint()¶

Accessor to equality constraints.

Returns:

equalityFunction: Describe equality constraints.

getInequalityConstraint()¶

Accessor to inequality constraints.

Returns:

inequalityFunction: Describe inequality constraints.

getLevelFunction()¶

Accessor to level function.

Returns:

levelFunction: Level function.

getLevelValue()¶

Accessor to level value.

Returns:

valuefloat: Level value.

getLinearConstraintBounds()¶

Accessor to the linear constraint bounds.

Only relevant for the linear problem type.

Returns:

LUInterval: Linear inequality constraint bounds.

getLinearConstraintCoefficients()¶

Accessor to the linear constraint term.

Only relevant for the linear problem type.

Returns:

AMatrix: Linear inequality constraint term.

getLinearCost()¶

Accessor to the linear cost.

Only relevant for the linear problem type.

Returns:

costPoint: Linear cost term.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getObjective()¶

Accessor to objective function.

Returns:

objectiveFunction: Objective function.

getResidualFunction()¶

Accessor to level function.

Returns:

levelFunction: Level function.

getVariablesType()¶

Accessor to the variables type.

Returns:

variablesTypeIndices: Types of the variables.

Notes

Possible values for each variable are ot.OptimizationProblemImplementation.CONTINUOUS, ot.OptimizationProblemImplementation.INTEGER and ot.OptimizationProblemImplementation.`BINARY`.

hasBounds()¶

Test whether bounds had been specified.

Returns:

valuebool: True if bounds had been set for this problem, False otherwise.

hasEqualityConstraint()¶

Test whether equality constraints had been specified.

Returns:

valuebool: True if equality constraints had been set for this problem, False otherwise.

hasInequalityConstraint()¶

Test whether inequality constraints had been specified.

Returns:

valuebool: True if inequality constraints had been set for this problem, False otherwise.

hasLevelFunction()¶

Test whether level function had been specified.

Returns:

valuebool: True if level function had been set for this problem, False otherwise.

hasMultipleObjective()¶

Test whether objective function is a scalar or vector function.

Returns:

valuebool: False if objective function is scalar, True otherwise.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasResidualFunction()¶

Test whether a least-square problem is defined.

Returns:

valuebool: True if this is a least-squares problem, False otherwise.

isContinuous()¶

Check if the problem is continuous.

Returns:

isContinuousbool: Returns True if all variables are continuous.

isLinear()¶

Check if the problem is linear.

Returns:

isLinearbool: Returns True if the problem is of linear type.

isMinimization(marginalIndex=0)¶

Test whether this is a minimization or maximization problem.

Parameters:

marginal_indexint, default=0: Index of the output marginal (for multi-objective only)

Returns:

valuebool: True if this is a minimization problem (default), False otherwise.

setBounds(bounds)¶

Accessor to bounds.

Parameters:

boundsInterval: Problem bounds.

setEqualityConstraint(equalityConstraint)¶

Accessor to equality constraints.

Parameters:

equalityConstraintFunction: Equality constraints.

setInequalityConstraint(inequalityConstraint)¶

Accessor to inequality constraints.

Parameters:

inequalityConstraintFunction: Inequality constraints.

setLevelFunction(levelFunction)¶

Accessor to level function.

Parameters:

levelFunctionFunction: Level function.

setLevelValue(levelValue)¶

Accessor to level value.

Parameters:

levelValuefloat: Level value.

setLinearConstraint(constraintCoefficients, LU)¶

Accessor to the linear constraint term.

Returns:

AMatrix: Linear inequality constraint term.
cbInterval: Linear inequality constraint bounds.

setLinearCost(cost)¶

Accessor to the linear cost.

Parameters:

costPoint: Linear cost term.

setMinimization(minimization, marginalIndex=0)¶

Tell whether this is a minimization or maximization problem.

Parameters:

minimizationbool: True if this is a minimization problem, False otherwise.
marginal_indexint, default=0: Index of the output marginal (for multi-objective only)

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setObjective(objective)¶

Accessor to objective function.

Parameters:

objectiveFunctionFunction: Objective function.

Notes

Constraints and bounds are cleared if the objective has a different input dimension in order to keep the problem valid at all time.

setResidualFunction(residualFunction)¶

Accessor to level function.

Parameters:

levelFunctionFunction: Level function.

setVariablesType(variableType)¶

Accessor to the variables type.

Parameters:

variablesTypeIndices: Types of the variables.

Notes

Possible values for each variable are ot.OptimizationProblemImplementation.CONTINUOUS, ot.OptimizationProblemImplementation.INTEGER and ot.OptimizationProblemImplementation.BINARY.

Examples using the class¶

Optimization using HiGHS solver

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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LinearProblem¶

Examples using the class¶