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Solving csdl problems

Define a problem in csdl​

This example does not intend to cover the features of csdl. For more details and tutorials on csdl, please refer to csdl documentation. In this example, we solve a constrained problem given by

minimizex1,x2∈Rx12+x22subject tox1≥0x1+x2=1x1−x2≥1\underset{x_1, x_2 \in \mathbb{R}}{\text{minimize}} \quad x_1^2 + x_2^2 \newline \text{subject to} \quad x_1 \geq 0 \newline \quad \quad \quad \quad x_1 + x_2 = 1 \newline \quad \quad \quad \quad x_1 - x_2 \geq 1

We know the solution of this problem is x1=1x_1=1, and x2=0x_2=0. However, we start from an intial guess of x1=0x_1=0, and x2=0.0x_2=0.0 for the purposes of this tutorial.

The problem model is written in csdl as follows:

from csdl import Model

# minimize x^2 + y^2 subject to x>=0, x+y=1, x-y>=1.

class QuadraticFunc(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**2 + y**2

        # 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.)

Once your model is setup in csdl, create a Simulator object in csdl and translate the Simulator object to a CSDLProblem object in modOpt.

from csdl_om import Simulator

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

from modopt import CSDLProblem

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

Once your problem is translated to modOpt, import your preferred optimizer from the respective library in modOpt and solve it, following the standard procedure. Here we will use the SLSQP optimizer from the scipy library.

from modopt import SLSQP

# Setup your preferred optimizer (SLSQP) with the Problem object 
# Pass in the options for your chosen optimizer
optimizer = SLSQP(prob, solver_options={'maxiter':20})

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

# Solve your optimization problem
optimizer.solve()

# Print results of optimization
optimizer.print_results()

1 . SLSQP​

Import the SLSQP optimizer as shown below:

from modopt import SLSQP

Options available can be found from the scipy docs. Options could be set by just passing them as kwargs when instantiating the SLSQP optimizer object. For example, we can set the maximum number of iterations maxiter and the precision goal ftol for the objective as shown below.

optimizer = SLSQP(prob, solver_options={'maxiter':20, 'ftol':1e-6})

2. SQP​

Import the SQP optimizer as shown below:

from modopt import SQP

Options available are: maxiter, opt_tol, and feas_tol. Options could be set by just passing them as kwargs when instantiating the SQP optimizer object. For example, we can set the maximum number of iterations maxiter and the optimality tolerance opt_tol shown below.

optimizer = SQP(prob, maxiter=20, opt_tol=1e-8)

3. SNOPT​

Import the SNOPT optimizer as shown below:

from modopt import SNOPT

Options could be set by just passing them as kwargs when instantiating the SNOPT optimizer object.

snopt_options = {
    'Major iterations': 100, 
    'Major optimality': 1e-9, 
    'Major feasibility': 1e-8
    }
optimizer = SNOPT(prob, solver_options=snopt_options)