[peterfirefly]

Getting tripped up by this is like seeing Cyrillic letters in an intro book on Russian and believing those are the hard parts of learning Russian.

As others have said: it's actually fairly straightforward and clear. That paragraph states exactly what they mean by "a mathematical optimization problem".

A simpler version that you might have seen in Calculus for Jocks is one where you are supposed to find the optimum of a single-variate function with no further constraints -- just find the largest or smallest value. You would look for places where the tangent is horizontal (by differentiating) + you would look at the "ends" (by looking at limits).

"Here the vector x..." tells us that this cost function is a bit more complicated: you are not looking for a single input value but a vector of many input values.

"subject to fi(x) <= bi" tells us that there are constraints and what language the authors will use to describe those constraints.

It's really all fairly standard and simple. The hard parts come later.