The optimization problem is best described as the search for a local maximum or minimum value of a scalar-valued function f(x). This search can be performed for all possible input values in the domain of f (and in this case, we refer to this problem as an unconstrained optimization), or for a specific subset of it that is expressible by a finite set of identities and inequalities (and we refer to this other problem as a constrained optimization). In this section, we are going to explore both modalities in several settings.
We focus on the search for the local minima of a function f(x) in an interval [a, b] (the search for local maxima can then be regarded as the search of the local minima of the function –f(x) in the same interval). For this task, we have the routine minimize_scalar in the module scipy.optimize. It accepts as obligatory input a univariate function f(x), together with a search method.
Most search methods are based...