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)\[\mathop {\min }\limits_x f\left( x \right)\]

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 \(f\left(x\right)\) 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