Turn non-convex constraint into a convex one


I hope everyone is doing well.

I ran into a problem! It is not a software issue. Assume that we have a constraint as (Convex>=Constant), which is a non-convex constraint.
I was wondering, is there any transformation/approximation I could do to turn this into a convex-constraint?
I do not want to use Taylor approximation since this specific constraint involves quadratic terms!

Methods like defining a slack variable or something else would be very intriguing to me.

Thanks a lot

No guarantees this will work well, or at all, on your problem.

Thank you so much for introducing this topic.

My problem is || W+Z ||_F^2 >= Constant (Frobenius norm of the sum of two matrices) where W and Z are both optimization variables. This is a non convex constraint.

I was wondering if there is any related topic to my problem that I can turn it into a convex constraint.

What you ask is impossible.

As @Erling wrote, that is impossible. But you can try, with NO guarantees of success, to do something similar to what Stephen Boyd described in his linked (above) answer.

However, i suggest you use a non-convex solver to solve your problem.If the dimension is small enough, you might even succeed in globally optimizing it with a branch and bound global optimizer. YALMIP provides several solver options to handle such a problem, or you can call solvers such as FMINCON (local optimizer) or BARON (branch and bound global optimizer) directly from MATLAB.