# 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.

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

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()


Methods

 List of dlib available optimization algorithms. Accessor to the object's name. Accessor to the object's id. Accessor to initialTrustRegionRadius parameter. Accessor to maxLineSearchIterations parameter. Accessor to maxSize parameter. Accessor to maximum allowed absolute error. Accessor to maximum allowed constraint error. Accessor to maximum allowed number of evaluations. Accessor to maximum allowed number of iterations. Accessor to maximum allowed relative error. Accessor to maximum allowed residual error. Accessor to the object's name. Accessor to optimization problem. Accessor to optimization result. Accessor to the object's shadowed id. Accessor to starting point. Accessor to the verbosity flag. Accessor to the object's visibility state. Accessor to wolfeRho parameter. Accessor to wolfeSigma parameter. Test if the object is named. Test if the object has a distinguishable name. Performs the actual optimization process. Accessor to initialTrustRegionRadius parameter, sets the value to use during optimization process. 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. setMaximumConstraintError(maximumConstraintError) Accessor to maximum allowed constraint error. 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. Set up a progress callback. setResult(result) Accessor to optimization result. 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. 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.
 getAlgorithmName setAlgorithmName
__init__(*args)
static GetAlgorithmNames()

List of dlib available optimization algorithms.

Returns:
algorithmNamesDescription

List of the names of available dlib search strategies.

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.

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

Returns:

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 where and 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 where is the current approximation of the optimum and 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 if , else .

getMaximumResidualError()

Accessor to maximum allowed residual error.

Returns:
maximumResidualErrorfloat

Maximum allowed residual error, where the residual error is defined by if , else .

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.

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.

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.

hasVisibleName()

Test if the object has a distinguishable name.

Returns:
hasVisibleNamebool

True if the name is not empty and not the default one.

run()

Performs the actual optimization process. Results are stored in the OptimizationResult parameter of the Dlib object.

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:

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 where and 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 where is the current approximation of the optimum and 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 if , else .

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.

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)
...     return True
>>> 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.

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

Optimization using dlib