NearestPointProblem¶

class NearestPointProblem(*args)¶

Nearest point problem.

This defines a nearest point problem:

$\min_{x} \frac{1}{2}\|x\|_2^2 \\ g(x) = v$

where $\| \cdot\|_2$ is the euclidian norm.

In other words, this is a minimum norm problem with a general nonlinear constraint.

Parameters

levelFunction: The level function $g$ .
valuefloat: The level value $v$ .

Examples

Define an optimization problem to find the point $(x_1, x_2, x_3, x_4)$ with minimum euclidian norm which satisfies $x_1+2x_2-3x_3+4x_4=3$ .

>>> import openturns as ot
>>> levelFunction = ot.SymbolicFunction(
...     ['x1', 'x2', 'x3', 'x4'], ['x1+2*x2-3*x3+4*x4'])
>>> problem = ot.NearestPointProblem(levelFunction, 3.0)

Methods

`getBounds`()	Accessor to bounds.
`getClassName`()	Accessor to the object's name.
`getDimension`()	Accessor to input dimension.
`getEqualityConstraint`()	Accessor to equality constraints.
`getId`()	Accessor to the object's id.
`getInequalityConstraint`()	Accessor to inequality constraints.
`getLevelFunction`()	Accessor to level function.
`getLevelValue`()	Accessor to level value.
`getName`()	Accessor to the object's name.
`getObjective`()	Accessor to objective function.
`getResidualFunction`()	Accessor to level function.
`getShadowedId`()	Accessor to the object's shadowed id.
`getVariablesType`()	Accessor to the variables type.
`getVisibility`()	Accessor to the object's visibility state.
`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.
`hasVisibleName`()	Test if the object has a distinguishable name.
`isContinuous`()	Check if the problem is continuous.
`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.
`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.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setVariablesType`(variableType)	Accessor to the variables type.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

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.

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

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.

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.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

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`.

getVisibility()¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

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.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool: True if the name is not empty and not the default one.

isContinuous()¶

Check if the problem is continuous.

Returns

isContinuousbool: Returns True if all variables are continuous.

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.

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.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

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.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

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