## I want to implement the support for the new convex problem of the log function, i.e., log (e^e^x-1) as following:

## x=-40:0.5:6;

y=log(exp(exp(x))-1);

plot(x,y,‘r-’);

This log function is convex, though it belongs to “log-convex” except of “log convex monomial” and “log convex posynomial”.

## Therefore, I want to implement the code to solve the following convex problem:

## cvx_begin

variables r

minimize( t-r );

subject to

log(exp(exp®)-1)<=t+10000;

cvx_end

Obviously, this convex problem is not supported by the current cvx version.

I could implement the function “exp(exp®)-1” using the epigraph.

However, how to improve the code in basis to solve this convex

problem?