7. Optimization with CSDL models

Problem:

\[\begin{split} \begin{align} \underset{x, y \in \mathbb{R}}{\text{minimize}} & \quad x^4 + y^4 \\ \text{subject to} & \quad x\geq0, \\ & \quad x+y=1, \\ & \quad x-y\geq1. \end{align} \end{split}\]

from csdl import Model

# minimize x^4 + y^4 subject to x>=0, x+y=1, x-y>=1.

class QuarticFunc(Model):
    def initialize(self):
        pass

    def define(self):
        # add_inputs
        x = self.create_input('x', val=1.)
        y = self.create_input('y', val=1.)

        z = x**4 + y**4

        # add_outputs
        self.register_output('z', z)

        constraint_1 = x + y
        constraint_2 = x - y
        self.register_output('constraint_1', constraint_1)
        self.register_output('constraint_2', constraint_2)

        # define optimization problem
        self.add_design_variable('x', lower=0.)
        self.add_design_variable('y')
        self.add_objective('z')
        self.add_constraint('constraint_1', equals=1.)
        self.add_constraint('constraint_2', lower=1.)


if __name__ == "__main__":
    # from csdl_om import Simulator
    from python_csdl_backend import Simulator

    # Create a Simulator object for your model
    sim = Simulator(QuarticFunc())

    from modopt import CSDLProblem

    # Instantiate your problem using the csdl Simulator object and name your problem
    prob = CSDLProblem(problem_name='quartic',simulator=sim)

    from modopt import SQP, SLSQP, SNOPT, PySLSQP

    # Setup your preferred optimizer (here, SLSQP) with the Problem object 
    # Pass in the options for your chosen optimizer
    optimizer = PySLSQP(prob, solver_options={'maxiter': 20, 'acc':1e-6})
    # optimizer = SLSQP(prob, solver_options={'maxiter':20, 'ftol':1e-6})
    # optimizer = SQP(prob, maxiter=20)
    snopt_options = {
        'Infinite bound': 1.0e20, 
        'Verify level': 3,
        'Verbose': True,
        }
    # optimizer = SNOPT(prob, solver_options=snopt_options)

    # Check first derivatives at the initial guess, if needed
    # optimizer.check_first_derivatives(prob.x0)
    # sim.run()
    # sim.check_totals()

    # Solve your optimization problem
    optimizer.solve()

    # Print results of optimization (summary_table contains information from each iteration)
    optimizer.print_results(summary_table=True)

    print(sim['x'])
    print(sim['y'])
    print(sim['z'])

/Users//modopt/modopt/external_libraries/snopt/snoptc.py:6: UserWarning: snoptc from 'optimize' could not be imported
  warnings.warn("snoptc from 'optimize' could not be imported")
/Users//modopt/modopt/external_libraries/snopt/snoptc.py:10: UserWarning: snopt7_python from 'optimize.solvers' could not be imported
  warnings.warn("snopt7_python from 'optimize.solvers' could not be imported")
/Users//modopt/modopt/external_libraries/snopt/snopt_optimizer.py:6: UserWarning: SNOPT_options from 'optimize' could not be imported
  warnings.warn("SNOPT_options from 'optimize' could not be imported")

Deleting self.pFpx ...
Deleting self.pCpx, pCpx_dict ...
Computing objective >>>>>>>>>>
---------Computed objective---------
Computing constraints >>>>>>>>>>
---------Computed constraints---------
Computing gradient >>>>>>>>>>
(('constraint_1', 'constraint_2', 'z'), ('x', 'y'))  not found, generating...

generating: DERIVATIVESconstraint_1,constraint_2,z-->x,y
constraint_1--> (1/5) |........                                |
constraint_2--> (1/5) |........                                |
z-->            (3/5) |........................                |
---------Computed gradient---------
Computing Jacobian >>>>>>>>>>
---------Computed Jacobian---------
Computing objective >>>>>>>>>>
---------Computed objective---------
Computing constraints >>>>>>>>>>
---------Computed constraints---------
Computing gradient >>>>>>>>>>
---------Computed gradient---------
Computing Jacobian >>>>>>>>>>
---------Computed Jacobian---------
Optimization terminated successfully    (Exit mode 0)
            Final objective value                : 1.000000e+00
            Final optimality                     : 3.002483e-15
            Final feasibility                    : 1.110223e-16
            Number of major iterations           : 2
            Number of function evaluations       : 2
            Number of derivative evaluations     : 2
            Average Derivative evaluation time   : 0.000222 s per evaluation
            Average Function evaluation time     : 0.000989 s per evaluation
            Total Function evaluation time       : 0.000443 s [  5.62%]
            Total Derivative evaluation time     : 0.001979 s [ 25.07%]
            Optimizer time                       : 0.000843 s [ 10.68%]
            Processing time                      : 0.004627 s [ 58.63%]
            Visualization time                   : 0.000000 s [  0.00%]
            Total optimization time              : 0.007892 s [100.00%]
            Summary saved to                     : slsqp_summary.out
[1.]
[1.11022302e-16]
[1.]

/Users//modopt/modopt/external_libraries/csdl/csdl_problem.py:53: UserWarning: This version of CSDL or python_csdl_backend does not support SURF paradigm.
  warnings.warn('This version of CSDL or python_csdl_backend does not support SURF paradigm.')
/Users//modopt/modopt/external_libraries/pyslsqp/pyslsqp.py:132: UserWarning: PySLSQP prints the final results by default. To suppress the results, set `solver_options={"iprint":0}`. Check the summary file "slsqp_summary.out" for the summary of optimization.
  warnings.warn('PySLSQP prints the final results by default. '