Cobyla

class Cobyla(*args)

Constrained Optimization BY Linear Approximations solver.

Available constructors:

Cobyla(problem)

Cobyla(problem, rhoBeg)

Parameters:
problemOptimizationProblem

Optimization problem to solve.

rhoBegfloat

A reasonable initial change to the variables.

See also

AbdoRackwitz, SQP, TNC, NLopt

Notes

It constructs successive linear approximations of the objective function and constraints via a simplex of d+1 points, and optimizes these approximations in a trust region at each step. This solver use no derivative information and supports all types of constraints.

Examples

>>> import openturns as ot
>>> model = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3*E*I)'])
>>> problem = ot.NearestPointProblem(model, 5.0)
>>> algo = ot.Cobyla(problem)
>>> algo.setMaximumEvaluationNumber(10000)
>>> algo.setStartingPoint([1.0] * 4)
>>> algo.run()
>>> result = algo.getResult()

Methods

getClassName()

Accessor to the object's name.

getId()

Accessor to the object's id.

getIgnoreFailure()

Accessor to ignore failure flag.

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.

getProblem()

Accessor to optimization problem.

getResult()

Accessor to optimization result.

getRhoBeg()

Accessor to rhoBeg parameter.

getShadowedId()

Accessor to the object's shadowed id.

getStartingPoint()

Accessor to starting point.

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.

setIgnoreFailure(ignoreFailure)

Accessor to ignore failure flag.

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.

setProblem(problem)

Accessor to optimization problem.

setProgressCallback(*args)

Set up a progress callback.

setResult(result)

Accessor to optimization result.

setRhoBeg(rhoBeg)

Accessor to rhoBeg parameter.

setShadowedId(id)

Accessor to the object's shadowed id.

setStartingPoint(startingPoint)

Accessor to starting point.

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)
getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

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.

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.

getProblem()

Accessor to optimization problem.

Returns:
problemOptimizationProblem

Optimization problem.

getResult()

Accessor to optimization result.

Returns:
resultOptimizationResult

Result class.

getRhoBeg()

Accessor to rhoBeg parameter.

Returns:
rhoBegfloat

A reasonable initial change to the variables.

getShadowedId()

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getStartingPoint()

Accessor to starting point.

Returns:
startingPointPoint

Starting point.

getVerbose()

Accessor to the verbosity flag.

Returns:
verbosebool

Verbosity flag state.

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.

setIgnoreFailure(ignoreFailure)

Accessor to ignore failure flag.

Parameters:
ignore_failurebool

Whether to ignore failure return codes.

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

setRhoBeg(rhoBeg)

Accessor to rhoBeg parameter.

Parameters:
rhoBegfloat

A reasonable initial change to the variables.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters:
idint

Internal unique identifier.

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

Accessor to the verbosity flag.

Parameters:
verbosebool

Verbosity flag state.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters:
visiblebool

Visibility flag.

Examples using the class

Use the post-analytical importance sampling algorithm

Use the post-analytical importance sampling algorithm

Estimate a flooding probability

Estimate a flooding probability

Use the Importance Sampling algorithm

Use the Importance Sampling algorithm

Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points

Use the FORM - SORM algorithms

Use the FORM - SORM algorithms

Test the design point with the Strong Maximum Test

Test the design point with the Strong Maximum Test

Axial stressed beam : comparing different methods to estimate a probability

Axial stressed beam : comparing different methods to estimate a probability

An illustrated example of a FORM probability estimate

An illustrated example of a FORM probability estimate

Optimization with constraints

Optimization with constraints

Control algorithm termination

Control algorithm termination

Quick start guide to optimization

Quick start guide to optimization

Optimization of the Rastrigin test function

Optimization of the Rastrigin test function