1
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1answer
22 views

Confusion related to the convexity of a bunch of functions

I have this confusion related to the convexity of some function.I was reading this paper - www.sigkdd.org/sites/default/files/issues/V14-01-02-Ye.pdf‎. I have this graph consisting of nodes denoted by ...
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3answers
66 views

Concave function divided by a convex function. What is the result?

Let us say that I have a function $f(x)$ that we know is a concave. And let us also say that we have another function $g(x)$ that is a convex. If I make a new function, $h(x) = \frac{f(x)}{g(x)}$, ...
1
vote
1answer
49 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
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0answers
49 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
907 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) ...