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.
levelFunction: Level function.
valuefloat: Level value.

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)

Define an optimization problem to find the point with minimum norm which satisfies $x1+2*x2-3*x3+4*x4=3$ .

>>> 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`(self)	Accessor to bounds.
`getClassName`(self)	Accessor to the object’s name.
`getDimension`(self)	Accessor to input dimension.
`getEqualityConstraint`(self)	Accessor to equality constraints.
`getId`(self)	Accessor to the object’s id.
`getImplementation`(self)	Accessor to the underlying implementation.
`getInequalityConstraint`(self)	Accessor to inequality constraints.
`getLevelFunction`(self)	Accessor to level function.
`getLevelValue`(self)	Accessor to level value.
`getName`(self)	Accessor to the object’s name.
`getObjective`(self)	Accessor to objective function.
`getResidualFunction`(self)	Accessor to the residual function.
`getVariablesType`(self)	Accessor to the variables type.
`hasBounds`(self)	Test whether bounds had been specified.
`hasEqualityConstraint`(self)	Test whether equality constraints had been specified.
`hasInequalityConstraint`(self)	Test whether inequality constraints had been specified.
`hasLevelFunction`(self)	Test whether level function had been specified.
`hasMultipleObjective`(self)	Test whether objective function is a scalar or vector function.
`hasResidualFunction`(self)	Test whether a least-square problem is defined.
`isContinuous`(self)	Check if the problem is continuous.
`isMinimization`(self)	Test whether this is a minimization or maximization problem.
`setBounds`(self, bounds)	Accessor to bounds.
`setEqualityConstraint`(self, equalityConstraint)	Accessor to equality constraints.
`setInequalityConstraint`(self, …)	Accessor to inequality constraints.
`setLevelFunction`(self, levelFunction)	Accessor to level function.
`setLevelValue`(self, levelValue)	Accessor to level value.
`setMinimization`(self, minimization)	Tell whether this is a minimization or maximization problem.
`setName`(self, name)	Accessor to the object’s name.
`setObjective`(self, objective)	Accessor to objective function.
`setResidualFunction`(self, residualFunction)	Accessor to the residual function.
`setVariablesType`(self, variableType)	Accessor to the variables type.

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

getBounds(self)¶

Accessor to bounds.

Returns

boundsInterval: Problem bounds.

getClassName(self)¶

Accessor to the object’s name.

Returns

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

getDimension(self)¶

Accessor to input dimension.

Returns

dimensionint: Input dimension of objective function.

getEqualityConstraint(self)¶

Accessor to equality constraints.

Returns

equalityFunction: Describe equality constraints.

getId(self)¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getImplementation(self)¶

Accessor to the underlying implementation.

Returns

implImplementation: The implementation class.

getInequalityConstraint(self)¶

Accessor to inequality constraints.

Returns

inequalityFunction: Describe inequality constraints.

getLevelFunction(self)¶

Accessor to level function.

Returns

levelFunction: Level function.

getLevelValue(self)¶

Accessor to level value.

Returns

valuefloat: Level value.

getName(self)¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getObjective(self)¶

Accessor to objective function.

Returns

objectiveFunction: Objective function.

getResidualFunction(self)¶

Accessor to the residual function.

Returns

residualFunctionFunction: Residual function.

getVariablesType(self)¶

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(self)¶

Test whether bounds had been specified.

Returns

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

hasEqualityConstraint(self)¶

Test whether equality constraints had been specified.

Returns

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

hasInequalityConstraint(self)¶

Test whether inequality constraints had been specified.

Returns

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

hasLevelFunction(self)¶

Test whether level function had been specified.

Returns

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

hasMultipleObjective(self)¶

Test whether objective function is a scalar or vector function.

Returns

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

hasResidualFunction(self)¶

Test whether a least-square problem is defined.

Returns

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

isContinuous(self)¶

Check if the problem is continuous.

Returns

isContinuousbool: Returns True if all variables are continuous.

isMinimization(self)¶

Test whether this is a minimization or maximization problem.

Returns

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

setBounds(self, bounds)¶

Accessor to bounds.

Parameters

boundsInterval: Problem bounds.

setEqualityConstraint(self, equalityConstraint)¶

Accessor to equality constraints.

Parameters

equalityConstraintFunction: Equality constraints.

setInequalityConstraint(self, inequalityConstraint)¶

Accessor to inequality constraints.

Parameters

inequalityConstraintFunction: Inequality constraints.

setLevelFunction(self, levelFunction)¶

Accessor to level function.

Parameters

levelFunctionFunction: Level function.

setLevelValue(self, levelValue)¶

Accessor to level value.

Parameters

levelValuefloat: Level value.

setMinimization(self, minimization)¶

Tell whether this is a minimization or maximization problem.

Parameters

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

setName(self, name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setObjective(self, 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(self, residualFunction)¶

Accessor to the residual function.

Parameters

residualFunctionFunction: Residual function.

setVariablesType(self, 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.

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