Issue with Norm and log constraint

Nonconvex
Dec 17, 2020
D

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?

M

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!

D
Replying to #2

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

M

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