Convexrt log(1+x) to a convex function

How can I convert the concave function log(1+x) to a convex function

Take the negative of it. Of course, that’s a rather different function.

Or use a one term Taylor series approximation, x, which is convex (and concave). Of course,. the remainder term can be very large, and it’s not likely to be a very good thing to do in an optimization problem.

Face the music, log(1+x) is a concave function. Converting it into a convex function is more difficult than converting one dollar into a billion dollars in the stock market.

Not everything is convex. If God had made the world convex, there wouldn’t be convex optimization, there would just be optimization.

Ok, thanks a lot. Mark. Apart from Taylor series approximation, hope there will be another way to do it.

No. There is no way to do it.