SQP¶

class SQP(*args)¶

Sequential Quadratic Programming solver.

This solver uses second derivative information and can only be used to solve level function problems.

Available constructors:

SQP(problem)

SQP(problem, tau, omega, smooth)

Parameters:

problemOptimizationProblem: Optimization problem to solve.
taufloat: Multiplicative decrease of linear step.
omegafloat: Armijo factor.
smoothfloat: Growing factor in penalization term.

See also

AbdoRackwitz, Cobyla, TNC, NLopt

Notes

SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints.

Examples

>>> import openturns as ot
>>> model = ot.SymbolicFunction(['x1', 'x2', 'x3', 'x4'], ['x1*cos(x1)+2*x2*x3-3*x3+4*x3*x4'])
>>> problem = ot.NearestPointProblem(model, -0.5)
>>> algo = ot.SQP(problem)
>>> 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.
`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.
`getOmega`()	Accessor to omega parameter.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getShadowedId`()	Accessor to the object's shadowed id.
`getSmooth`()	Accessor to smooth parameter.
`getStartingPoint`()	Accessor to starting point.
`getTau`()	Accessor to tau 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.
`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.
`setOmega`(tau)	Accessor to omega parameter.
`setProblem`(problem)	Accessor to optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setSmooth`(tau)	Accessor to smooth parameter.
`setStartingPoint`(startingPoint)	Accessor to starting point.
`setStopCallback`(*args)	Set up a stop callback.
`setTau`(tau)	Accessor to tau parameter.
`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.

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.

getOmega()¶

Accessor to omega parameter.

Returns:

omegafloat: Armijo factor.

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getSmooth()¶

Accessor to smooth parameter.

Returns:

smoothfloat: Growing factor in penalization term.

getStartingPoint()¶

Accessor to starting point.

Returns:

startingPointPoint: Starting point.

getTau()¶

Accessor to tau parameter.

Returns:

taufloat: Multiplicative decrease of linear step.

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.

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.

setOmega(tau)¶

Accessor to omega parameter.

Parameters:

omegafloat: Armijo factor.

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.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setSmooth(tau)¶

Accessor to smooth parameter.

Parameters:

smoothfloat: Growing factor in penalization term.

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()

setTau(tau)¶

Accessor to tau parameter.

Parameters:

taufloat: Multiplicative decrease of linear step.

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¶

Time variant system reliability problem

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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SQP¶

Examples using the class¶