Log(1+x^1.5) in cvx

My function is log(1+x^1.5).

Even though log(1+x^1.5) is concave, cvx can’t solve it because x^1.5 is convex.

So I changed x^1.5 to exp(1.5log(x)) but it’s log-concave so when I write 1+exp(1.5log(x)), cvx gave me an error Illegal operation: {log-concave} + {real constant}.

Is there any way to add real constant and log-concave?

And if not, is there any way to express log(1+x^1.5) in cvx?

Thank you!

log(1+x^1.5) is convex for x <= (1/2)^(2/3), and concave for x >= (1/2)^(2/3)

Even if your problem were constrained to be on only one of these sides, log(1+x^1.5) is not concave or convex over the entirety of its natural domain (x >= 0), so it’s unlikely there would be a CVX representation valid on even that side.

You’re not the first one on this forum to make an invalid claim of convexity (or concavity). Unfortunately, you are not likely to be the last.

Oops, you’re right.

It is not actually the original form of my function but I should have checked it.

I am so sorry and thank you for the reply.