Source code for openmdao.examples.paraboloid_optimize_constrained
""" Constrained optimization of the paraboloid component."""
from __future__ import print_function
from openmdao.api import IndepVarComp, Component, Problem, Group, ExecComp, ScipyOptimizer
[docs]class Paraboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
[docs] def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3"""
x = params['x']
y = params['y']
unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
[docs] def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = 2.0*x - 6.0 + y
J['f_xy', 'y'] = 2.0*y + 8.0 + x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
# Constraint Equation
root.add('con', ExecComp('c = x-y'))
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
root.connect('p.x', 'con.x')
root.connect('p.y', 'con.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-50, upper=50)
top.driver.add_desvar('p2.y', lower=-50, upper=50)
top.driver.add_objective('p.f_xy')
top.driver.add_constraint('con.c', lower=15.0)
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
# Expected Output
# Minimum of -27.083333 found at (7.166667, -7.833333)