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

`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`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.
`getOmega`()	Accessor to omega parameter.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getSmooth`()	Accessor to smooth parameter.
`getStartingPoint`()	Accessor to starting point.
`getTau`()	Accessor to tau parameter.
`hasName`()	Test if the object is named.
`run`()	Launch the optimization.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`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.
`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.
`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.

getMaximumEvaluationNumber
setMaximumEvaluationNumber

__init__(*args)¶

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__).

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.

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.

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.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

run()¶: Launch the optimization.

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.

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.

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.setMaximumCallsNumber(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.

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.setMaximumCallsNumber(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.

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¶