Differentiators

A differentiator is a special object that can be used by a driver to calculate the first or second derivatives of a workflow. The derivatives are calculated from the parameter inputs to the objective and constraint outputs. Any driver that has been decorated with the add_delegate decorator containing the UsesGradients or UsesHessians delegates contains a socket (i.e., Instance trait) called Differentiator. This socket can take a Differentiator object.

FiniteDifference

The FiniteDifference differentiator provides the gradient vector and Hessian matrix of the workflow using the finite difference method. For first derivatives, you have a choice between forward, backward, and central differences. Second derivatives are calculated using the standard three-point difference for both on-diagonal and off-diagonal terms.

The FiniteDifference differentiator can be used with the CONMIN and NEWSUMT optimizers by plugging it into the differentiator socket.

from openmdao.main.api import Assembly
from openmdao.lib.drivers.api import NEWSUMTdriver
from openmdao.lib.differentiators.finite_difference import FiniteDifference
from openmdao.examples.simple.paraboloid import Paraboloid

class OptimizationConstrained(Assembly):
    """Constrained optimization of the Paraboloid."""

    def __init__(self):
        """ Creates a new Assembly containing a Paraboloid and an optimizer"""

        super(OptimizationConstrained, self).__init__()

        # Create Paraboloid component instances
        self.add('paraboloid', Paraboloid_Derivative())

        # Create Optimizer instance
        self.add('driver', NEWSUMTdriver())

        # Driver process definition
        self.driver.workflow.add('paraboloid')

        # Differentiator
        self.driver.differentiator = FiniteDifference(self.driver)
        self.driver.differentiator.form = 'central'
        self.driver.differentiator.default_stepsize = .0001

        # Objective
        self.driver.add_objective('paraboloid.f_xy')

        # Design Variables
        self.driver.add_parameter('paraboloid.x', low=-50., high=50., fd_step=.01)
        self.driver.add_parameter('paraboloid.y', low=-50., high=50.)

        # Constraints
        self.driver.add_constraint('paraboloid.x-paraboloid.y >= 15.0')

The only argument that FiniteDifference takes is the driver you are plugging into.

There are two additional control variables for FiniteDifference. The form parameter is used to declare whether central, backward, or forward differencing will be used for the first derivative. The default_stepsize parameter is used to set a default finite difference step size. Note that you can declare a separate finite difference step size for each parameter in the call to add_parameter. Here, the finite difference step size for the input 'x' to paraboloid is set to .01. If you don’t specify fd_step for a parameter, then the default step size is used.

Fake Finite Difference is fully supported by the finite difference generator.

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