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.

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.

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.

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.

setVariablesType(variableType)

Accessor to the variables type.

__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.

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.

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.

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.

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.