About the convexity of function


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.

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.

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,

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.

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