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.
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.