TNC¶

class TNC(*args)¶

Truncated Newton Constrained solver.

Tunrcated-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.
specificParametersTNCSpecificParameters: Parameters for this solver.
scalesequence of float: Scaling factors to apply to each variables
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

See also

AbdoRackwitz, SQP, Cobyla, NLopt

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.
`getClassName`()	Accessor to the object's name.
`getEta`()	Accessor to eta parameter.
`getFmin`()	Accessor to fmin parameter.
`getId`()	Accessor to the object's id.
`getIgnoreFailure`()	Accessor to ignore failure flag.
`getMaxCGit`()	Accessor to maxCGit parameter.
`getMaximumAbsoluteError`()	Accessor to maximum allowed absolute error.
`getMaximumConstraintError`()	Accessor to maximum allowed constraint error.
`getMaximumEvaluationNumber`()	Accessor to maximum allowed number of evaluations.
`getMaximumIterationNumber`()	Accessor to maximum allowed number of iterations.
`getMaximumRelativeError`()	Accessor to maximum allowed relative error.
`getMaximumResidualError`()	Accessor to maximum allowed residual error.
`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.
`getShadowedId`()	Accessor to the object's shadowed id.
`getStartingPoint`()	Accessor to starting point.
`getStepmx`()	Accessor to stepmx parameter.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`run`()	Launch the optimization.
`setAccuracy`(accuracy)	Accessor to accuracy parameter.
`setEta`(eta)	Accessor to eta parameter.
`setFmin`(fmin)	Accessor to fmin parameter.
`setIgnoreFailure`(ignoreFailure)	Accessor to ignore failure flag.
`setMaxCGit`(maxCGit)	Accessor to maxCGit parameter.
`setMaximumAbsoluteError`(maximumAbsoluteError)	Accessor to maximum allowed absolute error.
`setMaximumConstraintError`(maximumConstraintError)	Accessor to maximum allowed constraint error.
`setMaximumEvaluationNumber`(...)	Accessor to maximum allowed number of evaluations.
`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.
`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.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setStartingPoint`(startingPoint)	Accessor to starting point.
`setStepmx`(stepmx)	Accessor to stepmx parameter.
`setStopCallback`(*args)	Set up a stop callback.
`setVisibility`(visible)	Accessor to the object's visibility state.

getVerbose
setVerbose

__init__(*args)¶

getAccuracy()¶

Accessor to accuracy parameter.

Returns:

accuracyfloat

Relative precision for finite difference calculations

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

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.

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getIgnoreFailure()¶

Accessor to ignore failure flag.

Returns:

ignore_failurebool: Whether to ignore failure return codes.

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.

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)

getMaximumEvaluationNumber()¶

Accessor to maximum allowed number of evaluations.

Returns:

Nint: Maximum allowed number of evaluations.

getMaximumIterationNumber()¶

Accessor to maximum allowed number of iterations.

Returns:

Nint: 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 $\epsilon^r_n=-1$ .

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.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

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.

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: True if the name is not empty and not the default one.

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).

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.

setIgnoreFailure(ignoreFailure)¶

Accessor to ignore failure flag.

Parameters:

ignore_failurebool: Whether to ignore failure return codes.

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.

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)

setMaximumEvaluationNumber(maximumEvaluationNumber)¶

Accessor to maximum allowed number of evaluations.

Parameters:

Nint: Maximum allowed number of evaluations.

setMaximumIterationNumber(maximumIterationNumber)¶

Accessor to maximum allowed number of iterations.

Parameters:

Nint: 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 $\epsilon^r_n=-1$ .

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.setMaximumEvaluationNumber(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.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

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.setMaximumEvaluationNumber(10000)
>>> def ask_stop():
...     return True
>>> solver.setStopCallback(ask_stop)
>>> solver.run()