ABSTRACT
The theory and practice of continuous optimization relies heavily on the basic notions and tools of real analysis. In this chapter we review important topics from analysis that we shall need later.
When we say that we seek the minimum value of a function f(x) over x within some set C we imply that there is a point z in C such that f(z) ≤ f(x) for all x in C. Of course, this need not be the case. For example, take the function f(x) = x defined on the real numbers and C the set of positive real numbers. In such cases, instead of looking for the minimum of f(x) over x in C, we may seek the infimum or greatest lower bound of the values f(x), over x in C.
