Optimization using NLopt

In this example we are going to explore optimization using OpenTURNS’ NLopt interface.

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)

List available algorithms

for algo in ot.NLopt.GetAlgorithmNames():
    print(algo)

Out:

AUGLAG
AUGLAG_EQ
GD_MLSL
GD_MLSL_LDS
GN_CRS2_LM
GN_DIRECT
GN_DIRECT_L
GN_DIRECT_L_NOSCAL
GN_DIRECT_L_RAND
GN_DIRECT_L_RAND_NOSCAL
GN_DIRECT_NOSCAL
GN_ESCH
GN_ISRES
GN_MLSL
GN_MLSL_LDS
GN_ORIG_DIRECT
GN_ORIG_DIRECT_L
G_MLSL
G_MLSL_LDS
LD_AUGLAG
LD_AUGLAG_EQ
LD_CCSAQ
LD_LBFGS
LD_MMA
LD_SLSQP
LD_TNEWTON
LD_TNEWTON_PRECOND
LD_TNEWTON_PRECOND_RESTART
LD_TNEWTON_RESTART
LD_VAR1
LD_VAR2
LN_AUGLAG
LN_AUGLAG_EQ
LN_BOBYQA
LN_COBYLA
LN_NELDERMEAD
LN_NEWUOA
LN_NEWUOA_BOUND
LN_PRAXIS
LN_SBPLX

More details on NLopt algorithms are available here .

The optimization algorithm is instanciated from the NLopt name

algo = ot.NLopt('LD_SLSQP')

define the problem

objective = ot.SymbolicFunction(['x1', 'x2'], ['100*(x2-x1^2)^2+(1-x1)^2'])
inequality_constraint = ot.SymbolicFunction(['x1', 'x2'], ['x1-2*x2'])
dim = objective.getInputDimension()
bounds = ot.Interval([-3.] * dim, [5.] * dim)
problem = ot.OptimizationProblem(objective)
problem.setMinimization(True)
problem.setInequalityConstraint(inequality_constraint)
problem.setBounds(bounds)

solve the problem

algo.setProblem(problem)
startingPoint = [0.0] * dim
algo.setStartingPoint(startingPoint)
algo.run()

retrieve results

result = algo.getResult()
print('x^=', result.getOptimalPoint())

Out:

x^= [0.517441,0.258721]

draw optimal value history

graph = result.drawOptimalValueHistory()
view = viewer.View(graph)
plt.show()