NLopt¶

class NLopt(*args)¶

Interface to NLopt.

This class exposes the solvers from the non-linear optimization library [nlopt2009].

More details about available algorithms are available here.

Parameters:

problemOptimizationProblem: Optimization problem to solve.
algoNamestr: The NLopt identifier of the algorithm. Use GetAlgorithmNames() to list available names.

See also

AbdoRackwitz, Cobyla, SQP, TNC

Notes

Here are some properties of the different algorithms:

Algorithm	Derivative info	Constraint support
AUGLAG	no derivative	all
AUGLAG_EQ	no derivative	all
GD_MLSL	first derivative	bounds required
GD_MLSL_LDS	first derivative	bounds required
GD_STOGO (disabled)	first derivative	bounds required
GD_STOGO_RAND (disabled)	first derivative	bounds required
GN_AGS (disabled)	no derivative	bounds required, inequality
GN_CRS2_LM	no derivative	bounds required
GN_DIRECT	no derivative	bounds required
GN_DIRECT_L	no derivative	bounds required
GN_DIRECT_L_NOSCAL	no derivative	bounds required
GN_DIRECT_L_RAND	no derivative	bounds required
GN_DIRECT_L_RAND_NOSCAL	no derivative	bounds required
GN_ESCH	no derivative	bounds required
GN_ISRES	no derivative	bounds required, all
GN_MLSL	no derivative	bounds required
GN_MLSL_LDS	no derivative	bounds required
GN_ORIG_DIRECT	no derivative	bounds required, inequality
GN_ORIG_DIRECT_L	no derivative	bounds required, inequality
G_MLSL	no derivative	bounds required
G_MLSL_LDS	no derivative	bounds required
LD_AUGLAG	first derivative	all
LD_AUGLAG_EQ	first derivative	all
LD_CCSAQ	first derivative	bounds, inequality
LD_LBFGS	first derivative	bounds
LD_MMA	first derivative	bounds, inequality
LD_SLSQP	first derivative	all
LD_TNEWTON	first derivative	bounds
LD_TNEWTON_PRECOND	first derivative	bounds
LD_TNEWTON_PRECOND_RESTART	first derivative	bounds
LD_TNEWTON_RESTART	first derivative	bounds
LD_VAR1	first derivative	bounds
LD_VAR2	first derivative	bounds
LN_AUGLAG	no derivative	all
LN_AUGLAG_EQ	no derivative	all
LN_BOBYQA	no derivative	bounds
LN_COBYLA	no derivative	all
LN_NELDERMEAD	no derivative	bounds
LN_NEWUOA	no derivative	none
LN_NEWUOA_BOUND (disabled)	no derivative	bounds
LN_PRAXIS (disabled)	no derivative	bounds
LN_SBPLX	no derivative	bounds

Availability of algorithms marked as optional may vary depending on the NLopt version or compilation options used.

Examples

>>> import openturns as ot
>>> dim = 4
>>> bounds = ot.Interval([-3.0] * dim, [5.0] * dim)
>>> linear = ot.SymbolicFunction(['x1', 'x2', 'x3', 'x4'], ['x1+2*x2-3*x3+4*x4'])
>>> problem = ot.OptimizationProblem(linear, ot.Function(), ot.Function(), bounds)
>>> print(ot.NLopt.GetAlgorithmNames())  
[AUGLAG,AUGLAG_EQ,GD_MLSL,GD_MLSL_LDS,...
>>> algo = ot.NLopt(problem, 'LD_MMA')  
>>> algo.setStartingPoint([0.0] * 4)  
>>> algo.run()  
>>> result = algo.getResult()  
>>> x_star = result.getOptimalPoint()  
>>> y_star = result.getOptimalValue()  

Methods

`GetAlgorithmNames`()	Accessor to the list of algorithms provided by NLopt, by names.
`getAlgorithmName`()	Accessor to the algorithm name.
`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`getInitialStep`()	Initial local derivative-free algorithms step accessor.
`getLocalSolver`()	Local solver accessor.
`getMaximumAbsoluteError`()	Accessor to maximum allowed absolute error.
`getMaximumCallsNumber`()	Accessor to maximum allowed number of calls.
`getMaximumConstraintError`()	Accessor to maximum allowed constraint error.
`getMaximumIterationNumber`()	Accessor to maximum allowed number of iterations.
`getMaximumRelativeError`()	Accessor to maximum allowed relative error.
`getMaximumResidualError`()	Accessor to maximum allowed residual error.
`getMaximumTimeDuration`()	Accessor to the maximum duration.
`getName`()	Accessor to the object's name.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getSeed`()	Random generator seed accessor.
`getStartingPoint`()	Accessor to starting point.
`hasName`()	Test if the object is named.
`run`()	Launch the optimization.
`setAlgorithmName`(algoName)	Accessor to the algorithm name.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`setInitialStep`(initialStep)	Initial local derivative-free algorithms step accessor.
`setLocalSolver`(localSolver)	Local solver accessor.
`setMaximumAbsoluteError`(maximumAbsoluteError)	Accessor to maximum allowed absolute error.
`setMaximumCallsNumber`(maximumCallsNumber)	Accessor to maximum allowed number of calls
`setMaximumConstraintError`(maximumConstraintError)	Accessor to maximum allowed constraint error.
`setMaximumIterationNumber`(maximumIterationNumber)	Accessor to maximum allowed number of iterations.
`setMaximumRelativeError`(maximumRelativeError)	Accessor to maximum allowed relative error.
`setMaximumResidualError`(maximumResidualError)	Accessor to maximum allowed residual error.
`setMaximumTimeDuration`(maximumTime)	Accessor to the maximum duration.
`setName`(name)	Accessor to the object's name.
`setProblem`(problem)	Accessor to optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setSeed`(seed)	Random generator seed accessor.
`setStartingPoint`(startingPoint)	Accessor to starting point.
`setStopCallback`(*args)	Set up a stop callback.

getMaximumEvaluationNumber
setMaximumEvaluationNumber

__init__(*args)¶

static GetAlgorithmNames()¶

Accessor to the list of algorithms provided by NLopt, by names.

Returns:

namesDescription: List of algorithm names provided by NLopt, according to its naming convention.

Examples

>>> import openturns as ot
>>> print(ot.NLopt.GetAlgorithmNames())  
[AUGLAG,AUGLAG_EQ,GD_MLSL,...

getAlgorithmName()¶

Accessor to the algorithm name.

Returns:

algoNamestr: The NLopt identifier of the algorithm.

getCheckStatus()¶

Accessor to check status flag.

Returns:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

getClassName()¶

Accessor to the object’s name.

Returns:

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

getInitialStep()¶

Initial local derivative-free algorithms step accessor.

Returns:

dxPoint: The initial step.

getLocalSolver()¶

Local solver accessor.

Returns:

solverNLopt: The local solver.

getMaximumAbsoluteError()¶

Accessor to maximum allowed absolute error.

Returns:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

getMaximumCallsNumber()¶

Accessor to maximum allowed number of calls.

Returns:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

getMaximumConstraintError()¶

Accessor to maximum allowed constraint error.

Returns:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

getMaximumIterationNumber()¶

Accessor to maximum allowed number of iterations.

Returns:

maximumIterationNumberint: Maximum allowed number of iterations.

getMaximumRelativeError()¶

Accessor to maximum allowed relative error.

Returns:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumResidualError()¶

Accessor to maximum allowed residual error.

Returns:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

getMaximumTimeDuration()¶

Accessor to the maximum duration.

Returns:

maximumTimefloat: Maximum optimization duration in seconds.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getSeed()¶

Random generator seed accessor.

Returns:

seedint: Seed.

getStartingPoint()¶

Accessor to starting point.

Returns:

startingPointPoint: Starting point.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

run()¶: Launch the optimization.

setAlgorithmName(algoName)¶

Accessor to the algorithm name.

Parameters:

algoNamestr: The NLopt identifier of the algorithm.

setCheckStatus(checkStatus)¶

Accessor to check status flag.

Parameters:

checkStatusbool: Whether to check the termination status. If set to False, run() will not throw an exception if the algorithm does not fully converge and will allow one to still find a feasible candidate.

setInitialStep(initialStep)¶

Initial local derivative-free algorithms step accessor.

Parameters:

dxsequence of float: The initial step.

setLocalSolver(localSolver)¶

Local solver accessor.

Parameters:

solverNLopt: The local solver.

setMaximumAbsoluteError(maximumAbsoluteError)¶

Accessor to maximum allowed absolute error.

Parameters:

maximumAbsoluteErrorfloat: Maximum allowed absolute error, where the absolute error is defined by $\epsilon^a_n=\|\vect{x}_{n+1}-\vect{x}_n\|_{\infty}$ where $\vect{x}_{n+1}$ and $\vect{x}_n$ are two consecutive approximations of the optimum.

setMaximumCallsNumber(maximumCallsNumber)¶

Accessor to maximum allowed number of calls

Parameters:

maximumEvaluationNumberint: Maximum allowed number of direct objective function calls through the () operator. Does not take into account eventual indirect calls through finite difference gradient calls.

setMaximumConstraintError(maximumConstraintError)¶

Accessor to maximum allowed constraint error.

Parameters:

maximumConstraintErrorfloat: Maximum allowed constraint error, where the constraint error is defined by $\gamma_n=\|g(\vect{x}_n)\|_{\infty}$ where $\vect{x}_n$ is the current approximation of the optimum and $g$ is the function that gathers all the equality and inequality constraints (violated values only)

setMaximumIterationNumber(maximumIterationNumber)¶

Accessor to maximum allowed number of iterations.

Parameters:

maximumIterationNumberint: Maximum allowed number of iterations.

setMaximumRelativeError(maximumRelativeError)¶

Accessor to maximum allowed relative error.

Parameters:

maximumRelativeErrorfloat: Maximum allowed relative error, where the relative error is defined by $\epsilon^r_n=\epsilon^a_n/\|\vect{x}_{n+1}\|_{\infty}$ if $\|\vect{x}_{n+1}\|_{\infty}\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumResidualError(maximumResidualError)¶

Accessor to maximum allowed residual error.

Parameters:

maximumResidualErrorfloat: Maximum allowed residual error, where the residual error is defined by $\epsilon^r_n=\frac{\|f(\vect{x}_{n+1})-f(\vect{x}_{n})\|}{\|f(\vect{x}_{n+1})\|}$ if $\|f(\vect{x}_{n+1})\|\neq 0$ , else $\epsilon^r_n=-1$ .

setMaximumTimeDuration(maximumTime)¶

Accessor to the maximum duration.

Parameters:

maximumTimefloat: Maximum optimization duration in seconds.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setProblem(problem)¶

Accessor to optimization problem.

Parameters:

problemOptimizationProblem: Optimization problem.

setProgressCallback(*args)¶

Set up a progress callback.

Can be used to programmatically report the progress of an optimization.

Parameters:

callbackcallable: Takes a float as argument as percentage of progress.

Examples

>>> import sys
>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> solver.setProgressCallback(report_progress)
>>> solver.run()

setResult(result)¶

Accessor to optimization result.

Parameters:

resultOptimizationResult: Result class.

setSeed(seed)¶

Random generator seed accessor.

Parameters:

seedint: The RNG seed.

Notes

The default is set by the NLopt-InitialSeed ResourceMap entry.

setStartingPoint(startingPoint)¶

Accessor to starting point.

Parameters:

startingPointPoint: Starting point.

setStopCallback(*args)¶

Set up a stop callback.

Can be used to programmatically stop an optimization.

Parameters:

callbackcallable: Returns an int deciding whether to stop or continue.

Examples

>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> solver = ot.OptimizationAlgorithm(problem)
>>> solver.setStartingPoint([0, 0])
>>> solver.setMaximumResidualError(1.e-3)
>>> solver.setMaximumCallsNumber(10000)
>>> def ask_stop():
...     return True
>>> solver.setStopCallback(ask_stop)
>>> solver.run()