"Suppose we want to numerically calculate the global maximum a real function f attains over a compact, convex subinterval of the real number line..."
I am trying to decipher the following, but need help figuring out how to read this para aloud:
Suppose we want to numerically calculate the global maximum of the function ,
with and with being a compact and convex interval. Assume that is strictly
concave on . If we know that the global maximum lies in the interior of ...
So far, I would translate it as "Suppose we want to numerically calculate the global maximum of the function f for which X is comprised of real numbers and X is a subset of real numbers....
I don't know what the rest means or even if I've got the first part right.
I meant is a subset of X :P
Also, every interval in R is convex, so that definition isn't necessary here.
f being strictly concave means, not formally, that its graph will have a concave shape (think of something like the back of a spoon). Another explanation is that for every 2 points, the graph of f will lie "above" the line joining those two points. You can see a good visualization of this here: Concave function - Wikipedia, the free encyclopedia
I'm comfortable with the concave function bit.