# Issue with Norm and log constraint

I have two constraints in the form

\log(1+\sum_{j=1}^{10}|b_j|^2+|a|^2)\ge \log(2)x_k+y_k, \forall k

and

1+\sum_{j=1}^{10}|b_j|^2 \le e^{y_k^{(0)}}(y_k-y_k^{(0)}+1), \forall k

Here, x_k, y_k are optimization variables. The elements a and b_j are functions for some other variables.

How can I express them in CVX?

log of norm is neither convex nor concave.

It is time for you to carefully reread Why isn't CVX accepting my model? READ THIS FIRST!

Hi, Unfortunately, my problem statement is not correct. I have edited it. Please have look.

My answer is the same as in my previous post. And that includes the 2nd paragraph in that post.