Unconstrained optimization

1. Unconstrained optimization#

In this chapter, we’ll cover how to apply scipy.optimize.minimize to unconstrained optimization problems. As a reminder, unconstrained optimization considers:

(1.1)#minx⁡f(x)

with:

  • x: the design variable of length n

  • f: the objective function.

Method#

In this course, we’re making use of the function scipy.optimize.minimize. The documentation of this function is available here: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html [The SciPy community, 2024]. In this course we’ll cover only the relevant parts.

For unconstrained optimization we need to run at least scipy.optimize.minimize(fun, x0, ...) with:

  • fun, the objective function f(x) to be minimized. fun is a callable. The scipy.optimize.minimize function takes care of defining and inputting our design variable x.

  • x0, the initial guess for our design variable x. It needs to be a ndarray with length n

The function scipy.optimize.minimize outputs an object scipy.optimize.OptimizeResult. with:

  • scipy.optimize.OptimizeResult.x the optimized solution of the design variable x. It is a ndarray with length n

  • scipy.optimize.OptimizeResult.success, a indication whether or not the optimizer was executed successfully. It is a bool, indicating True or False

  • scipy.optimize.OptimizeResult.message, a message describing the cause of termination of the optimization algorithm. It is a str.

  • scipy.optimize.OptimizeResult.fun, the values of the optimized objective function f. It is a int or float

  • scipy.optimize.OptimizeResult.nit, the number of iteration performed by the optimizer. It is a int

Test Yourself

Questions, discussions and comments#

Contents