Can CVX handle jointly convex functions?

Can CVX handle jointly convex functions? If so, why do many papers carry out first-order Taylor expansions for jointly convex functions?

I hope someone can help me. This problem has been bothering me for a long time.

CVX can handle ONLY jointly convex functions. In fact it can handle only some special carefully selected examples of jointly convex functions.

Many thanks for your answer.

Now that CVX can handle joint convex functions, why do many papers carry out Taylor expansion for jointly convex functions?

Is it because it can only handle part of the jointly convex functions like you said?

Maybe. You would have to check the examples or ask the authors of those papers.

Maybe the Taylor series is used for functions which are not jointly convex.

For instance, difference of convex f1(x) - f2(x) where f1(x) is convex, but f2(x) is concave (or is at least not convex). Then, first-order Taylor series might be applied to f2(x).