Ipopt¶
- class Ipopt(*args)¶
Ipopt nonlinear optimization solver.
Ipopt is a software package for large-scale nonlinear optimization.
- Parameters:
- problem
OptimizationProblem
, optional Optimization problem to solve. Default is an empty problem.
- problem
See also
Notes
Algorithms parameters:
Ipopt algorithms can be adapted using numerous parameters, described here. These parameters can be modified using the
ResourceMap
. For every optionoptionName
, one simply add a key namedIpopt-optionName
with the value to use, as shown below:>>> import openturns as ot >>> ot.ResourceMap.AddAsUnsignedInteger('Ipopt-print_level', 5) >>> ot.ResourceMap.AddAsScalar('Ipopt-diverging_iterates_tol', 1e15)
Convergence criteria:
To estimate the convergence of the algorithm during the optimization process, Ipopt uses specific tolerance parameters, different from the standard absolute/relative/residual errors used in OpenTURNS. The definition of Ipopt’s parameters can be found in this paper, page 3.
Thus the attributes
maximumAbsoluteError
,maximumRelativeError
,maximumResidualError
andmaximumConstraintError
defined in’OptimizationAlgorithm
are not used in this case. The tolerances used by Ipopt can be set using specific options (e.g.tol
,dual_inf_tol
…).Examples
The code below ensures the optimization of the following problem:
subject to
>>> import openturns as ot
>>> # Definition of objective function >>> objectiveFunction = ot.SymbolicFunction(['x0','x1','x2','x3'], ['-x0 -x1 -x2'])
>>> # Definition of variables bounds >>> bounds = ot.Interval([0,0,0,0],[1,1e308,1e308,5],[True,True,True,True],[True,False,False,True])
Inequality constraints are defined by a function such that . The inequality expression above has to be modified to match this formulation.
>>> # Definition of constraints >>> h = ot.SymbolicFunction(['x0','x1','x2','x3'], ['-(x1-1/2)^2 - (x2-1/2)^2 + 1/4', '-x0 + x1', '-x0 - x2 - x3 + 2'])
>>> # Setting up Ipopt problem >>> problem = ot.OptimizationProblem(objectiveFunction) >>> problem.setBounds(bounds) >>> problem.setInequalityConstraint(h)
>>> algo = ot.Ipopt(problem) >>> algo.setStartingPoint([0,0,0,0]) >>> algo.setMaximumCallsNumber(1000) >>> algo.setMaximumIterationNumber(1000) >>> algo.setMaximumTimeDuration(5.0)
>>> # Running the solver >>> algo.run()
>>> # Retrieving the results >>> result = algo.getResult() >>> optimalPoint = result.getOptimalPoint() >>> optimalValue = result.getOptimalValue() >>> evaluationNumber = result.getInputSample().getSize()
Methods
Accessor to check status flag.
Accessor to the object's name.
Accessor to maximum allowed absolute error.
Accessor to maximum allowed number of calls.
Accessor to maximum allowed constraint error.
Accessor to maximum allowed number of iterations.
Accessor to maximum allowed relative error.
Accessor to maximum allowed residual error.
Accessor to the maximum duration.
getName
()Accessor to the object's name.
Accessor to optimization problem.
Accessor to optimization result.
Accessor to starting point.
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.
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.
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 where and 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 where is the current approximation of the optimum and 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 if , else .
- getMaximumResidualError()¶
Accessor to maximum allowed residual error.
- Returns:
- maximumResidualErrorfloat
Maximum allowed residual error, where the residual error is defined by if , else .
- 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:
- problem
OptimizationProblem
Optimization problem.
- problem
- getResult()¶
Accessor to optimization result.
- Returns:
- result
OptimizationResult
Result class.
- result
- 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 where and 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 where is the current approximation of the optimum and 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 if , else .
- setMaximumResidualError(maximumResidualError)¶
Accessor to maximum allowed residual error.
- Parameters:
- maximumResidualErrorfloat
Maximum allowed residual error, where the residual error is defined by if , else .
- 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:
- problem
OptimizationProblem
Optimization problem.
- 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:
- result
OptimizationResult
Result class.
- result
- setStartingPoint(startingPoint)¶
Accessor to starting point.
- Parameters:
- startingPoint
Point
Starting point.
- startingPoint
- 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()