optim

This module defines the interface for solving minimization problems:

\[minimize_x f(x)\]

where \(f : \mathbb R^n \to \mathbb R\).

Module Contents

type optim.ObjectiveFn = Callable[[np.ndarray, object], int]

Signature of the objective function \(f(, y)\).

!!!!!!!!! The function accepts four arguments: !!!!!!!!! - t: current time, !!!!!!!!! - y: state vector at time \(t\), !!!!!!!!! - ydot: output array to which the result !!!!!!!!! - user_data: additional context (user-defined data) that !!!!!!!!! must be passed to the function (e.g., parameters of the system).

class optim.Optim(impl: str)

Interface for solving optimization (minimization) problems.

This class serves as a gateway to the implementations of the solvers for optimization problems.

Parameters:

impl (str) – Name of the desired implementation.

Examples

Let’s solve the following convex optimization problem:

\[minimize \sum_{i = 1}^N x_i^2\]

where the solution is \([0, ..., 0]\) as the problem is convex.

First, import the necessary modules: >>> import numpy as np >>> from oif.interfaces.optim import Optim

Define the objective function:

>>> def objective_fn(x):
...     return np.sum(x**2)

Create an instance of the optim solver using the implementation “scipy_optimize”, which is an adapter to the scipy.optimize Python package:

>>> s = Optim("scipy_optimize")

We set the initial value, the right-hand side function, and the tolerance:

>>> s.set_initial_guess([2.718, 3.142])
>>> s.set_objective_fn(objective_fn)

Now we solve the minimization problem and print the return status and message:

>>> status, message = s.minimize()

We can print the resultant minimizer by retrieving it from the solver:

>>> print(f"Minimizer is {s.x}")

x0: numpy.ndarray

Current value of the state vector.

x: numpy.ndarray

user_data: object

oif_user_data: openinterfaces.core.OIFUserData

set_initial_guess(x0: numpy.ndarray)

Set initial guess for the optimization problem

set_objective_fn(objective_fn: ObjectiveFn)

set_user_data(user_data: object)

Specify additional data that will be used for right-hand side function.

set_method(method_name: str, method_params: dict = {})

Set integrator, if the name is recognizable.

minimize()

Integrate to time t and write solution to y.