# 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

LSQ

Least squares (best for large residual)

Least squares

First derivative

None

LSQLM

Least squares LM (small residual)

Least squares

First derivative

None

TrustRegion

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. Check if dlib functions are available for use in openturns. computeLagrangeMultipliers(self, x) Compute the Lagrange multipliers of a problem at a given point. getClassName(self) Accessor to the object’s name. getId(self) Accessor to the object’s id. Accessor to initialTrustRegionRadius parameter. Accessor to maxLineSearchIterations parameter. getMaxSize(self) 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. getName(self) Accessor to the object’s name. getProblem(self) Accessor to optimization problem. getResult(self) Accessor to optimization result. getShadowedId(self) Accessor to the object’s shadowed id. Accessor to starting point. getVerbose(self) Accessor to the verbosity flag. getVisibility(self) Accessor to the object’s visibility state. getWolfeRho(self) Accessor to wolfeRho parameter. getWolfeSigma(self) Accessor to wolfeSigma parameter. hasName(self) Test if the object is named. hasVisibleName(self) Test if the object has a distinguishable name. run(self) Performs the actual optimization process. setInitialTrustRegionRadius(self, radius) Accessor to initialTrustRegionRadius parameter, sets the value to use during optimization process. setMaxLineSearchIterations(self, …) Accessor to maxLineSearchIterations parameter, sets the value to use during line search process. setMaxSize(self, maxSize) Accessor to maxSize parameter, sets the value to use during optimization process. setMaximumAbsoluteError(self, …) Accessor to maximum allowed absolute error. setMaximumConstraintError(self, …) Accessor to maximum allowed constraint error. setMaximumEvaluationNumber(self, …) Accessor to maximum allowed number of evaluations. setMaximumIterationNumber(self, …) Accessor to maximum allowed number of iterations. setMaximumRelativeError(self, …) Accessor to maximum allowed relative error. setMaximumResidualError(self, …) Accessor to maximum allowed residual error. setName(self, name) Accessor to the object’s name. setProblem(self, problem) Accessor to optimization problem. setProgressCallback(self, \*args) Set up a progress callback. setResult(self, result) Accessor to optimization result. setShadowedId(self, id) Accessor to the object’s shadowed id. setStartingPoint(self, startingPoint) Accessor to starting point. setStopCallback(self, \*args) Set up a stop callback. setVerbose(self, verbose) Accessor to the verbosity flag. setVisibility(self, visible) Accessor to the object’s visibility state. setWolfeRho(self, wolfeRho) Accessor to wolfeRho parameter, sets the value to use during line search process. setWolfeSigma(self, wolfeSigma) Accessor to wolfeSigma parameter, sets the value to use during line search process.
 getAlgorithmName setAlgorithmName
__init__(self, \*args)

Initialize self. See help(type(self)) for accurate signature.

static GetAlgorithmNames()

List of dlib available optimization algorithms.

Returns
algorithmNamesDescription

List of the names of available dlib search strategies.

static IsAvailable()

Check if dlib functions are available for use in openturns.

Returns
isAvailablebool

Whether dlib algorithms can be used or not.

computeLagrangeMultipliers(self, x)

Compute the Lagrange multipliers of a problem at a given point.

Parameters
xsequence of float

Point at which the Lagrange multipliers are computed.

Returns
lagrangeMultipliersequence of float

Lagrange multipliers of the problem at the given point.

Notes

The Lagrange multipliers are associated with the following Lagrangian formulation of the optimization problem:

where .

The Lagrange multipliers are stored as , where:
• is of dimension 0 if there is no equality constraint, else of dimension the dimension of ie the number of scalar equality constraints

• and are of dimension 0 if there is no bound constraint, else of dimension of

• is of dimension 0 if there is no inequality constraint, else of dimension the dimension of ie the number of scalar inequality constraints

The vector is solution of the following linear system:

If there is no constraint of any kind, is of dimension 0, as well as if no constraint is active.

getClassName(self)

Accessor to the object’s name.

Returns
class_namestr

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

getId(self)

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getInitialTrustRegionRadius(self)

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(self)

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(self)

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(self)

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(self)

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(self)

Accessor to maximum allowed number of evaluations.

Returns
Nint

Maximum allowed number of evaluations.

getMaximumIterationNumber(self)

Accessor to maximum allowed number of iterations.

Returns
Nint

Maximum allowed number of iterations.

getMaximumRelativeError(self)

Accessor to maximum allowed relative error.

Returns
maximumRelativeErrorfloat

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

getMaximumResidualError(self)

Accessor to maximum allowed residual error.

Returns
maximumResidualErrorfloat

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

getName(self)

Accessor to the object’s name.

Returns
namestr

The name of the object.

getProblem(self)

Accessor to optimization problem.

Returns
problemOptimizationProblem

Optimization problem.

getResult(self)

Accessor to optimization result.

Returns
resultOptimizationResult

Result class.

getShadowedId(self)

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getStartingPoint(self)

Accessor to starting point.

Returns
startingPointPoint

Starting point.

getVerbose(self)

Accessor to the verbosity flag.

Returns
verbosebool

Verbosity flag state.

getVisibility(self)

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

getWolfeRho(self)

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(self)

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(self)

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName(self)

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

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

run(self)

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

setInitialTrustRegionRadius(self, 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

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

setMaxLineSearchIterations(self, 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(self, 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(self, 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(self, 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(self, maximumEvaluationNumber)

Accessor to maximum allowed number of evaluations.

Parameters
Nint

Maximum allowed number of evaluations.

setMaximumIterationNumber(self, maximumIterationNumber)

Accessor to maximum allowed number of iterations.

Parameters
Nint

Maximum allowed number of iterations.

setMaximumRelativeError(self, maximumRelativeError)

Accessor to maximum allowed relative error.

Parameters
maximumRelativeErrorfloat

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

setMaximumResidualError(self, maximumResidualError)

Accessor to maximum allowed residual error.

Parameters
Maximum allowed residual error, where the residual error is defined by

if , else .

setName(self, name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setProblem(self, problem)

Accessor to optimization problem.

Parameters
problemOptimizationProblem

Optimization problem.

setProgressCallback(self, \*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.setMaximumIterationNumber(100)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> solver.setProgressCallback(report_progress)
>>> solver.run()

setResult(self, result)

Accessor to optimization result.

Parameters
resultOptimizationResult

Result class.

setShadowedId(self, id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setStartingPoint(self, startingPoint)

Accessor to starting point.

Parameters
startingPointPoint

Starting point.

setStopCallback(self, \*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.setMaximumIterationNumber(100)
...     return True
>>> solver.run()

setVerbose(self, verbose)

Accessor to the verbosity flag.

Parameters
verbosebool

Verbosity flag state.

setVisibility(self, visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.

setWolfeRho(self, 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(self, 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.