Minimizing a simple linear function
The most basic type of problem we face in optimization is finding the parameters where a function takes its minimum value. Usually, this problem is constrained by some bounds on the possible values of the parameters, which increases the complexity of the problem. Obviously, the complexity of this problem increases further if the function that we are minimizing is also complex. For this reason, we must first consider linear functions, which are in the following form:
To solve this kind of problem, we need to convert the constraints into a form that can be used by a computer. In this case, we usually convert them into a linear algebra problem (matrices and vectors). Once this is done, we can use the tools from the linear algebra packages in NumPy and SciPy to find the parameters we seek. Fortunately, since this kind of problem occur quite frequently, SciPy has routines that handle this conversion and subsequent solving.
In this recipe, we...
