About the convexity of function

Nonconvex
1

Hi,

I’m working on a problem about UAV energy consumption. I met a function about X. The function is P = 1 / sqrt( x*x + sqrt( x * x * x * x + 1)).

We can discuss the convexity of this function, express your opinion, and give the reason. I am looking forward to your reply.

2

As seen from the 2nd derivative, it changes convexity near 0.76. So even for x > 0, it is neither convex nor concave; so can’t be used in CVX.

Per the forum rules, you are supposed to tell us the convexity of functions, not the other way around.

3

Hi Mark,

Thank you very much for your reply. I’m not sure about the convexity of this function, so I want to discuss it with anybody. Can we determine the convexity of a function by only judging the positive and negative of 2nd derivation? If x > 0.76, is the function convex in this region?

Best regards,
Yanbo

4

You need to learn about the basics of convexity and convex optimization. This forum is not the place to do it.

You can try studying https://web.stanford.edu/~boyd/cvxbook/ if your math background is strong enough.

Perhaps post at https://math.stackexchange.com/ if you need some help on the basics.

5

Hi,
Thanks a lot. I learned a lot from your recommended links.