0
votes
1answer
42 views

Does the following relation always hold?

Given two functions $$f_1(x)=g_1(x)+h(x)$$ and $$f_2(x)=g_2(x)+h(x)$$ I know that $f_1(x)$ and $f_2(x)$ are monotone increasing. If $g_2(x)<g_3(x)<g_1(x)$, then is it true that ...
1
vote
0answers
43 views

why is it important to have $\max_x \min_y f(x,y)=\min_y \max_x f(x,y)$?

I am currently trying to understand the minimax theorem of Von Neumann and the improved versions of this theorem. At any case we have the property $$\max_{x\in X} \min_{y\in Y}f(x,y)=\min_{y\in Y} ...
0
votes
1answer
548 views

Is the variance of a convex function a convex function

I am working on a optimization-related research problem and need to know if the variance of a convex function is convex. I know this can be a little vague so I'm including a (rather formal) ...