```#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
***********************************************************************************
opt_tutorial3.py
DAE Tools: pyDAE module, www.daetools.com
***********************************************************************************
DAE Tools is free software; you can redistribute it and/or modify it under the
Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with the
DAE Tools software; if not, see <http://www.gnu.org/licenses/>.
************************************************************************************
"""
__doc__ = """
This tutorial introduces NLOPT NLP solver, its setup and options.
"""

import sys
from time import localtime, strftime
from daetools.pyDAE import *
from daetools.solvers.nlopt import pyNLOPT

class modTutorial(daeModel):
def __init__(self, Name, Parent = None, Description = ""):
daeModel.__init__(self, Name, Parent, Description)

self.x1 = daeVariable("x1", no_t, self)
self.x2 = daeVariable("x2", no_t, self)
self.x3 = daeVariable("x3", no_t, self)
self.x4 = daeVariable("x4", no_t, self)

self.dummy = daeVariable("dummy", no_t, self, "A dummy variable to satisfy the condition that there should be at least one-state variable and one equation in a model")

def DeclareEquations(self):
daeModel.DeclareEquations(self)

eq = self.CreateEquation("Dummy")
eq.Residual = self.dummy()

class simTutorial(daeSimulation):
def __init__(self):
daeSimulation.__init__(self)
self.m = modTutorial("opt_tutorial3")
self.m.Description = __doc__

def SetUpParametersAndDomains(self):
pass

def SetUpVariables(self):
self.m.x1.AssignValue(1)
self.m.x2.AssignValue(5)
self.m.x3.AssignValue(5)
self.m.x4.AssignValue(1)

def SetUpOptimization(self):
# Set the objective function (min)
self.ObjectiveFunction.Residual = self.m.x1() * self.m.x4() * (self.m.x1() + self.m.x2() + self.m.x3()) + self.m.x3()

# Set the constraints (inequality, equality)
# Constraints are in the following form:
#  - Inequality: g(i) <= 0
#  - Equality: h(i) = 0
c1 = self.CreateInequalityConstraint("Constraint 1") # g(x) >= 25:  25 - x1*x2*x3*x4 <= 0
c1.Residual = 25 - self.m.x1() * self.m.x2() * self.m.x3() * self.m.x4()

c2 = self.CreateEqualityConstraint("Constraint 2") # h(x) == 40
c2.Residual = self.m.x1() * self.m.x1() + self.m.x2() * self.m.x2() + self.m.x3() * self.m.x3() + self.m.x4() * self.m.x4() - 40

# Set the optimization variables, their lower/upper bounds and the starting point
self.SetContinuousOptimizationVariable(self.m.x1, 1, 5, 2);
self.SetContinuousOptimizationVariable(self.m.x2, 1, 5, 2);
self.SetContinuousOptimizationVariable(self.m.x3, 1, 5, 2);
self.SetContinuousOptimizationVariable(self.m.x4, 1, 5, 2);

def chooseAlgorithm():
from PyQt5 import QtWidgets
algorithms = ['NLOPT_GN_DIRECT','NLOPT_GN_DIRECT_L','NLOPT_GN_DIRECT_L_RAND','NLOPT_GN_DIRECT_NOSCAL','NLOPT_GN_DIRECT_L_NOSCAL',
'NLOPT_GN_DIRECT_L_RAND_NOSCAL','NLOPT_GN_ORIG_DIRECT','NLOPT_GN_ORIG_DIRECT_L','NLOPT_GD_STOGO','NLOPT_GD_STOGO_RAND',
'NLOPT_LD_LBFGS_NOCEDAL','NLOPT_LD_LBFGS','NLOPT_LN_PRAXIS','NLOPT_LD_VAR1','NLOPT_LD_VAR2','NLOPT_LD_TNEWTON',
'NLOPT_LD_TNEWTON_RESTART','NLOPT_LD_TNEWTON_PRECOND','NLOPT_LD_TNEWTON_PRECOND_RESTART','NLOPT_GN_CRS2_LM',
'NLOPT_GN_MLSL','NLOPT_GD_MLSL','NLOPT_GN_MLSL_LDS','NLOPT_GD_MLSL_LDS','NLOPT_LD_MMA','NLOPT_LN_COBYLA',
'NLOPT_LN_AUGLAG_EQ','NLOPT_LD_AUGLAG_EQ','NLOPT_LN_BOBYQA','NLOPT_GN_ISRES',
'NLOPT_AUGLAG','NLOPT_AUGLAG_EQ','NLOPT_G_MLSL','NLOPT_G_MLSL_LDS','NLOPT_LD_SLSQP']
# Show the input box to choose the algorithm (the default is len(algorithms)-1 that is: NLOPT_LD_SLSQP)
algorithm, ok = QtWidgets.QInputDialog.getItem(None, "NLOPT Algorithm", "Choose the NLOPT algorithm:", algorithms, len(algorithms)-1, False)
if ok:
return str(algorithm)
else:
return 'NLOPT_LD_SLSQP'

def run(**kwargs):
simulation = simTutorial()
# NLOPT algorithm must be set in its constructor
if guiRun:
algorithm = chooseAlgorithm()
nlpsolver = pyNLOPT.daeNLOPT(algorithm)
else:
nlpsolver = pyNLOPT.daeNLOPT('NLOPT_LD_SLSQP')
return daeActivity.optimize(simulation, reportingInterval   = 1,
timeHorizon         = 1,
nlpsolver           = nlpsolver,
reportSensitivities = True,
**kwargs)

if __name__ == "__main__":
app = daeCreateQtApplication(sys.argv)
guiRun = False if (len(sys.argv) > 1 and sys.argv[1] == 'console') else True
run(guiRun = guiRun, qtApp = app)
```