OptimizationProblem¶

class OptimizationProblem(*args)¶

Base class to define an optimization problem.

This represents a general optimization problem:

$\min_{x\in B} f(x) \\ g(x) = 0 \\ h(x) \ge 0$

where B is problem’s bounds, f is the objective function, g are equality constraints, and h are inequality constraints.

Available constructors:

OptimizationProblem(objective)

OptimizationProblem(objective, equality, inequality, bounds)

Parameters

objectiveFunction: Objective function. Additional constraints and bounds must always be consistent with the objective input dimension.
equalityFunction: Equality constraints.
inequalityFunction: Inequality constraints.
boundsInterval: Bounds.

Examples

Define an optimization problem to find the minimum of the Rosenbrock function:

>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)

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.
`getImplementation`()	Accessor to the underlying implementation.
`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 the residual 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.
`hasResidualFunction`()	Test whether a least-square problem is defined.
`isContinuous`()	Check if the problem is continuous.
`isMinimization`()	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)	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 the residual 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.

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getImplementation()¶

Accessor to the underlying implementation.

Returns

implImplementation: The implementation class.

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 the residual function.

Returns

residualFunctionFunction: Residual 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.

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()¶

Test whether this is a minimization or maximization problem.

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)¶

Tell whether this is a minimization or maximization problem.

Parameters

minimizationbool: True if this is a minimization problem, False otherwise.

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 the residual function.

Parameters

residualFunctionFunction: Residual 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.

OpenTURNS

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

Previous topic

Next topic

This Page

OptimizationProblem¶