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.
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.