Maybe,
"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
So X being a convex interval means that for any two points you choose in the X interval, the line between these points is a subset of X. Can you explain why that might be an important thing to state? What is the alternative? I'm just not getting the intuition here.
I'm comfortable with the concave function bit.
You can read on some uses of convexity here: Convex set - Wikipedia, the free encyclopedia
Other than that, I'm not very familiar with advanced concepts relying on convexity, so someone else can probably give you more information than I can.