Dlib¶

class Dlib(*args)¶

Base class for optimization solvers from the [dlib2009] library.

Available constructors:

Dlib(algoName)

Dlib(problem, algoName)

Parameters:

algoNamestr, optional: Identifier of the optimization method to use. Use GetAlgorithmNames() to list available algorithms. Default is ‘BFGS’.
problemOptimizationProblem, optional: Optimization problem to solve. Default is an empty problem.

Methods

`GetAlgorithmNames`()	List of dlib available optimization algorithms.
`getAlgorithmName`()	Accessor to the algorithm name.
`getCheckStatus`()	Accessor to check status flag.
`getClassName`()	Accessor to the object's name.
`getInitialTrustRegionRadius`()	Accessor to initialTrustRegionRadius parameter.
`getMaxLineSearchIterations`()	Accessor to maxLineSearchIterations parameter.
`getMaxSize`()	Accessor to maxSize 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.
`getProblem`()	Accessor to optimization problem.
`getResult`()	Accessor to optimization result.
`getStartingPoint`()	Accessor to starting point.
`getWolfeRho`()	Accessor to wolfeRho parameter.
`getWolfeSigma`()	Accessor to wolfeSigma parameter.
`hasName`()	Test if the object is named.
`run`()	Performs the actual optimization process.
`setAlgorithmName`(algoName)	Accessor to the algorithm name.
`setCheckStatus`(checkStatus)	Accessor to check status flag.
`setInitialTrustRegionRadius`(radius)	Accessor to initialTrustRegionRadius parameter, sets the value to use during optimization process.
`setMaxLineSearchIterations`(...)	Accessor to maxLineSearchIterations parameter, sets the value to use during line search process.
`setMaxSize`(maxSize)	Accessor to maxSize parameter, sets the value to use during optimization process.
`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.
`setProblem`(problem)	Accessor to optimization problem.
`setProgressCallback`(*args)	Set up a progress callback.
`setResult`(result)	Accessor to optimization result.
`setStartingPoint`(startingPoint)	Accessor to starting point.
`setStopCallback`(*args)	Set up a stop callback.
`setWolfeRho`(wolfeRho)	Accessor to wolfeRho parameter, sets the value to use during line search process.
`setWolfeSigma`(wolfeSigma)	Accessor to wolfeSigma parameter, sets the value to use during line search process.

See also

AbdoRackwitz, Cobyla, NLopt

Notes

The table below presents some properties of the available algorithms from dlib. Details on optimization methods are available on http://dlib.net/optimization.html

Algorithm	Description	Problem type support	Derivatives info	Constraint support
cg	Conjugate gradient	General	First derivative	Bounds
bfgs	BFGS	General	First derivative	Bounds
lbfgs	Limited memory BFGS	General	First derivative	Bounds
newton	Newton	General	First and second derivatives	Bounds
global	Global optimization	General	No derivative	Bounds needed
least_squares	Least squares (best for large residual)	Least squares	First derivative	None
least_squares_lm	Least squares LM (small residual)	Least squares	First derivative	None
trust_region	Trust region	General	No derivative	None

Derivatives are managed automatically by openturns, according to the available data (analytical formula or finite differences computation).

The global optimization algorithm requires finite fixed bounds for all input variables. In this strategy, the solver starts by refining a local extremum until no significant improvement is found. Then it tries to find better extrema in the rest of the domain defined by the user, until the maximum number of function evaluation is reached.

In least squares and trust region methods, the optimization process continues until the user criteria on absolute, relative and residual errors are satisfied, or until no significant improvement can be achieved.

Examples

Define an optimization problem to find the minimum of the Rosenbrock function:

>>> import openturns as ot
>>> rosenbrock = ot.SymbolicFunction(['x1', 'x2'], ['(1-x1)^2+100*(x2-x1^2)^2'])
>>> problem = ot.OptimizationProblem(rosenbrock)
>>> cgSolver = ot.Dlib(problem,'cg')  
>>> cgSolver.setStartingPoint([0, 0])  
>>> cgSolver.setMaximumResidualError(1.e-3)  
>>> cgSolver.setMaximumIterationNumber(100)  
>>> cgSolver.run()  
>>> result = cgSolver.getResult()  
>>> x_star = result.getOptimalPoint()  
>>> y_star = result.getOptimalValue()  

__init__(*args)¶

static GetAlgorithmNames()¶

List of dlib available optimization algorithms.

Returns:

algorithmNamesDescription: List of the names of available dlib search strategies.

getAlgorithmName()¶

Accessor to the algorithm name.

Returns:

algoNamestr: The identifier of the algorithm.

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__).

getInitialTrustRegionRadius()¶

Accessor to initialTrustRegionRadius parameter. Relevant for trust region, least squares and least squares LM algorithms only.

Returns:

initialTrustRegionRadiusfloat: The radius of the initial trust region used in optimization algorithms.

getMaxLineSearchIterations()¶

Accessor to maxLineSearchIterations parameter. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Returns:

maxLineSearchIterationsint: The maximum number of line search iterations to perform at each iteration of the optimization process. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

getMaxSize()¶

Accessor to maxSize parameter. Relevant for LBFGS algorithm only.

Returns:

maxSizeint: The maximum amount of memory used during optimization process. 10 is a typical value for maxSize. Relevant for LBFGS algorithm only.

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.

getProblem()¶

Accessor to optimization problem.

Returns:

problemOptimizationProblem: Optimization problem.

getResult()¶

Accessor to optimization result.

Returns:

resultOptimizationResult: Result class.

getStartingPoint()¶

Accessor to starting point.

Returns:

startingPointPoint: Starting point.

getWolfeRho()¶

Accessor to wolfeRho parameter. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Returns:

wolfeRhofloat: The value of the wolfeRho parameter used in the optimization process.

getWolfeSigma()¶

Accessor to wolfeSigma parameter. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Returns:

wolfeSigmafloat: The value of the wolfeSigma parameter used in the optimization process.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

run()¶: Performs the actual optimization process. Results are stored in the OptimizationResult parameter of the Dlib object.

setAlgorithmName(algoName)¶

Accessor to the algorithm name.

Parameters:

algoNamestr: The identifier of the algorithm.

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.

setInitialTrustRegionRadius(radius)¶

Accessor to initialTrustRegionRadius parameter, sets the value to use during optimization process. Relevant for trust region, least squares and least squares LM algorithms only.

Parameters:

initialTrustRegionRadiusfloat: The radius of the initial trust region to use in the optimization process.

setMaxLineSearchIterations(maxLineSearchIterations)¶

Accessor to maxLineSearchIterations parameter, sets the value to use during line search process. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Parameters:

maxLineSearchIterationsint: The value of the maxLineSearchIterations parameter to use in the optimization process.

setMaxSize(maxSize)¶

Accessor to maxSize parameter, sets the value to use during optimization process. Relevant for LBFGS algorithm only.

Parameters:

maxSizeint: The maximum amount of memory to use during optimization process. 10 is a typical value for maxSize. Relevant for LBFGS algorithm only.

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.

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.

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()

setWolfeRho(wolfeRho)¶

Accessor to wolfeRho parameter, sets the value to use during line search process. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Parameters:

wolfeRhofloat: The value of the wolfeRho parameter to use in the optimization process.

setWolfeSigma(wolfeSigma)¶

Accessor to wolfeSigma parameter, sets the value to use during line search process. Relevant for algorithms CG, BFGS/LBFGS and Newton only.

Parameters:

wolfeSigmafloat: The value of the wolfeSigma parameter to use in the optimization process.

Examples using the class¶

Optimization using dlib

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

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