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.

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.

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()

__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()