TNC

class TNC(*args)

Truncated Newton Constrained solver.

Truncated-Newton method Non-linear optimizer. This solver uses no derivative information and only supports bound constraints.

Available constructors:

TNC(problem)

TNC(problem, scale, offset, maxCGit, eta, stepmx, accuracy, fmin, rescale)

Parameters:
problemOptimizationProblem

Optimization problem to solve.

scalesequence of float

Scaling factors to apply to each variable.

offsetsequence of float

Constant to subtract to each variable.

maxCGitint

Maximum number of hessian*vector evaluation per main iteration.

etafloat

Severity of the line search.

stepmxfloat

Maximum step for the line search, may be increased during call.

accuracyfloat

Relative precision for finite difference calculations.

fminfloat

Minimum function value estimate.

rescalefloat

f scaling factor (in log10) used to trigger f value rescaling.

Examples

>>> import openturns as ot
>>> model = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3*E*I)'])
>>> bounds = ot.Interval([1.0]*4, [2.0]*4)
>>> problem = ot.OptimizationProblem(model, ot.Function(), ot.Function(), bounds)
>>> algo = ot.TNC(problem)
>>> algo.setStartingPoint([1.0] * 4)
>>> algo.run()
>>> result = algo.getResult()

Methods

getAccuracy()

Accessor to accuracy parameter.

getCheckStatus()

Accessor to check status flag.

getClassName()

Accessor to the object's name.

getEta()

Accessor to eta parameter.

getFmin()

Accessor to fmin parameter.

getMaxCGit()

Accessor to maxCGit parameter.

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.

getOffset()

Accessor to offset parameter.

getProblem()

Accessor to optimization problem.

getRescale()

Accessor to rescale parameter.

getResult()

Accessor to optimization result.

getScale()

Accessor to scale parameter.

getStartingPoint()

Accessor to starting point.

getStepmx()

Accessor to stepmx parameter.

hasName()

Test if the object is named.

run()

Launch the optimization.

setAccuracy(accuracy)

Accessor to accuracy parameter.

setCheckStatus(checkStatus)

Accessor to check status flag.

setEta(eta)

Accessor to eta parameter.

setFmin(fmin)

Accessor to fmin parameter.

setMaxCGit(maxCGit)

Accessor to maxCGit parameter.

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.

setOffset(offset)

Accessor to offset parameter.

setProblem(problem)

Accessor to optimization problem.

setProgressCallback(*args)

Set up a progress callback.

setRescale(rescale)

Accessor to rescale parameter.

setResult(result)

Accessor to optimization result.

setScale(scale)

Accessor to scale parameter.

setStartingPoint(startingPoint)

Accessor to starting point.

setStepmx(stepmx)

Accessor to stepmx parameter.

setStopCallback(*args)

Set up a stop callback.

getIgnoreFailure

getMaximumEvaluationNumber

setIgnoreFailure

setMaximumEvaluationNumber

__init__(*args)
getAccuracy()

Accessor to accuracy parameter.

Returns:
accuracyfloat

Relative precision for finite difference calculations

if <= machine_precision, set to sqrt(machine_precision).

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__).

getEta()

Accessor to eta parameter.

Returns:
etafloat

Severity of the line search.

if < 0 or > 1, set to 0.25.

getFmin()

Accessor to fmin parameter.

Returns:
fminfloat

Minimum function value estimate.

getMaxCGit()

Accessor to maxCGit parameter.

Returns:
maxCGitint

Maximum number of hessian*vector evaluation per main iteration

if maxCGit = 0, the direction chosen is -gradient

if maxCGit < 0, maxCGit is set to max(1,min(50,n/2)).

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.

getOffset()

Accessor to offset parameter.

Returns:
offsetPoint

Constant to subtract to each variable

if empty, the constant are (min-max)/2 for interval bounded

variables and x for the others.

getProblem()

Accessor to optimization problem.

Returns:
problemOptimizationProblem

Optimization problem.

getRescale()

Accessor to rescale parameter.

Returns:
rescalefloat

f scaling factor (in log10) used to trigger f value rescaling

if 0, rescale at each iteration

if a big value, never rescale

if < 0, rescale is set to 1.3.

getResult()

Accessor to optimization result.

Returns:
resultOptimizationResult

Result class.

getScale()

Accessor to scale parameter.

Returns:
scalePoint

Scaling factors to apply to each variable

if empty, the factors are min-max for interval bounded variables

and 1+|x] for the others.

getStartingPoint()

Accessor to starting point.

Returns:
startingPointPoint

Starting point.

getStepmx()

Accessor to stepmx parameter.

Returns:
stepmxfloat

Maximum step for the line search. may be increased during call

if too small, will be set to 10.0.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

run()

Launch the optimization.

setAccuracy(accuracy)

Accessor to accuracy parameter.

Parameters:
accuracyfloat

Relative precision for finite difference calculations

if <= machine_precision, set to sqrt(machine_precision).

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.

setEta(eta)

Accessor to eta parameter.

Parameters:
etafloat

Severity of the line search.

if < 0 or > 1, set to 0.25.

setFmin(fmin)

Accessor to fmin parameter.

Parameters:
fminfloat

Minimum function value estimate.

setMaxCGit(maxCGit)

Accessor to maxCGit parameter.

Parameters:
maxCGitint

Maximum number of hessian*vector evaluation per main iteration

if maxCGit = 0, the direction chosen is -gradient

if maxCGit < 0, maxCGit is set to max(1,min(50,n/2)).

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.

setOffset(offset)

Accessor to offset parameter.

Parameters:
offsetsequence of float

Constant to subtract to each variable

if empty, the constant are (min-max)/2 for interval bounded

variables and x for the others.

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()
setRescale(rescale)

Accessor to rescale parameter.

Parameters:
rescalefloat

f scaling factor (in log10) used to trigger f value rescaling

if 0, rescale at each iteration

if a big value, never rescale

if < 0, rescale is set to 1.3.

setResult(result)

Accessor to optimization result.

Parameters:
resultOptimizationResult

Result class.

setScale(scale)

Accessor to scale parameter.

Parameters:
scalesequence of float

Scaling factors to apply to each variable

if empty, the factors are min-max for interval bounded variables

and 1+|x] for the others.

setStartingPoint(startingPoint)

Accessor to starting point.

Parameters:
startingPointPoint

Starting point.

setStepmx(stepmx)

Accessor to stepmx parameter.

Parameters:
stepmxfloat

Maximum step for the line search. may be increased during call

if too small, will be set to 10.0.

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()

Examples using the class

Kriging: configure the optimization solver

Kriging: configure the optimization solver

Advanced Kriging

Advanced Kriging

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling

Linear Regression with interval-censored observations

Linear Regression with interval-censored observations

Mix/max search using optimization

Mix/max search using optimization