# TNC¶

class TNC(*args)

Truncated Newton Constrained solver.

Available constructors:

TNC(problem)

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

Parameters: problem : OptimizationProblem Optimization problem to solve. specificParameters : TNCSpecificParameters Parameters for this solver. scale : sequence of float Scaling factors to apply to each variables offset : sequence of float Constant to subtract to each variable maxCGit : int Maximum number of hessian*vector evaluation per main iteration eta : float Severity of the line search. stepmx : float Maximum step for the line search. may be increased during call accuracy : float Relative precision for finite difference calculations fmin : float Minimum function value estimate. rescale : float f scaling factor (in log10) used to trigger f value rescaling

Notes

Non-linear optimizer supporting bound constraints. This solver does not implement the progress callback.

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

 computeLagrangeMultipliers(x) Compute the Lagrange multipliers of a problem at a given point. 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. 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. getVerbose() Accessor to the verbosity flag. 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. 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. setVerbose(verbose) Accessor to the verbosity flag. setVisibility(visible) Accessor to the object’s visibility state.
__init__(*args)

Initialize self. See help(type(self)) for accurate signature.

computeLagrangeMultipliers(x)

Compute the Lagrange multipliers of a problem at a given point.

Parameters: x : sequence of float Point at which the Lagrange multipliers are computed. lagrangeMultiplier : sequence of float Lagrange multipliers of the problem at the given point.

Notes

The Lagrange multipliers are associated with the following Lagrangian formulation of the optimization problem:

where .

The Lagrange multipliers are stored as , where:
• is of dimension 0 if there is no equality constraint, else of dimension the dimension of ie the number of scalar equality constraints
• and are of dimension 0 if there is no bound constraint, else of dimension of
• is of dimension 0 if there is no inequality constraint, else of dimension the dimension of ie the number of scalar inequality constraints

The vector is solution of the following linear system:

If there is no constraint of any kind, is of dimension 0, as well as if no constraint is active.

getAccuracy()

Accessor to accuracy parameter.

Returns: accuracy : float Relative precision for finite difference calculations if <= machine_precision, set to sqrt(machine_precision).
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getEta()

Accessor to eta parameter.

Returns: eta : float Severity of the line search. if < 0 or > 1, set to 0.25.
getFmin()

Accessor to fmin parameter.

Returns: fmin : float Minimum function value estimate.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getMaxCGit()

Accessor to maxCGit parameter.

Returns: maxCGit : int 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: maximumAbsoluteError : float Maximum allowed absolute error.
getMaximumConstraintError()

Accessor to maximum allowed constraint error.

Returns: maximumConstraintError : float Maximum allowed constraint error.
getMaximumEvaluationNumber()

Accessor to maximum allowed number of evaluations.

Returns: N : int Maximum allowed number of evaluations.
getMaximumIterationNumber()

Accessor to maximum allowed number of iterations.

Returns: N : int Maximum allowed number of iterations.
getMaximumRelativeError()

Accessor to maximum allowed relative error.

Returns: maximumRelativeError : float Maximum allowed relative error.
getMaximumResidualError()

Accessor to maximum allowed residual error.

Returns: maximumResidualError : float Maximum allowed residual error.
getName()

Accessor to the object’s name.

Returns: name : str The name of the object.
getOffset()

Accessor to offset parameter.

Returns: offset : Point 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: problem : OptimizationProblem Optimization problem.
getRescale()

Accessor to rescale parameter.

Returns: rescale : float 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: result : OptimizationResult Result class.
getScale()

Accessor to scale parameter.

Returns: scale : Point 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: id : int Internal unique identifier.
getStartingPoint()

Accessor to starting point.

Returns: startingPoint : Point Starting point.
getStepmx()

Accessor to stepmx parameter.

Returns: stepmx : float Maximum step for the line search. may be increased during call if too small, will be set to 10.0.
getVerbose()

Accessor to the verbosity flag.

Returns: verbose : bool Verbosity flag state.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool True if the name is not empty and not the default one.
run()

Launch the optimization.

setAccuracy(accuracy)

Accessor to accuracy parameter.

Parameters: accuracy : float Relative precision for finite difference calculations if <= machine_precision, set to sqrt(machine_precision).
setEta(eta)

Accessor to eta parameter.

Parameters: eta : float Severity of the line search. if < 0 or > 1, set to 0.25.
setFmin(fmin)

Accessor to fmin parameter.

Parameters: fmin : float Minimum function value estimate.
setMaxCGit(maxCGit)

Accessor to maxCGit parameter.

Parameters: maxCGit : int 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: maximumAbsoluteError : float Maximum allowed absolute error.
setMaximumConstraintError(maximumConstraintError)

Accessor to maximum allowed constraint error.

Parameters: maximumConstraintError : float Maximum allowed constraint error.
setMaximumEvaluationNumber(maximumEvaluationNumber)

Accessor to maximum allowed number of evaluations.

Parameters: N : int Maximum allowed number of evaluations.
setMaximumIterationNumber(maximumIterationNumber)

Accessor to maximum allowed number of iterations.

Parameters: N : int Maximum allowed number of iterations.
setMaximumRelativeError(maximumRelativeError)

Accessor to maximum allowed relative error.

Parameters: maximumRelativeError : float Maximum allowed relative error.
setMaximumResidualError(maximumResidualError)

Accessor to maximum allowed residual error.

Parameters: maximumResidualError : float Maximum allowed residual error.
setName(name)

Accessor to the object’s name.

Parameters: name : str The name of the object.
setOffset(offset)

Accessor to offset parameter.

Parameters: offset : sequence 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: problem : OptimizationProblem Optimization problem.
setProgressCallback(*args)

Set up a progress callback.

Parameters: callback : callable Takes a float as argument as percentage of progress.

Notes

May not be implemented by all solvers, refer to the solver documentation.

setRescale(rescale)

Accessor to rescale parameter.

Parameters: rescale : float 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: result : OptimizationResult Result class.
setScale(scale)

Accessor to scale parameter.

Parameters: scale : sequence 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: id : int Internal unique identifier.
setStartingPoint(startingPoint)

Accessor to starting point.

Parameters: startingPoint : Point Starting point.
setStepmx(stepmx)

Accessor to stepmx parameter.

Parameters: stepmx : float 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.

Parameters: callback : callable Returns an int deciding whether to stop or continue.

Notes

May not be implemented by all solvers, refer to the solver documentation.

setVerbose(verbose)

Accessor to the verbosity flag.

Parameters: verbose : bool Verbosity flag state.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.