Optimization with constraints

In this example we are going to expose methods to solve a generic optimization problem in the form

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)

define the objective function

objective = ot.SymbolicFunction(['x1', 'x2', 'x3', 'x4'], [
                                'x1 + 2 * x2 - 3 * x3 + 4 * x4'])

define the constraints

inequality_constraint = ot.SymbolicFunction(
    ['x1', 'x2', 'x3', 'x4'], ['x1-x3'])

define the problem bounds

dim = objective.getInputDimension()
bounds = ot.Interval([-3.] * dim, [5.] * dim)

define the problem

problem = ot.OptimizationProblem(objective)
problem.setMinimization(True)
problem.setInequalityConstraint(inequality_constraint)
problem.setBounds(bounds)

solve the problem

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

retrieve results

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

Out:

x^= [5,-3,5,-3]

draw optimal value history

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