# TFOCS: The case of differentiable dual

(A follow up on question 703).)
Section 2.3 of the TFOCS journal paper discusses the case of a differentiable dual function. In that case, based on eqs. (2.4) and (2.5), it seems that the function f doesn’t have to be prox-capable but only “conj”-capable. Wouldn’t that case be relatively easy to implement in TFOCS using the existing primitives?

You’re talking about the journal article, not the user guide. (But I am grateful that you are reading it!)

If you know that your dual function is differentiable, then you have two choices. One, you can compute the dual yourself, using equation (2.5), and feed the dual directly into the standard tfocs routine. This is exactly what is discussed in Section 2.3.

Alternatively, you can use tfocs_SCD with a very small value of \mu. But honestly, the only way you are likely to know for sure if your dual function is differentiable is to actually compute it. And if you can do that, well, you might as well solve it directly.

(sorry, I fixed the link) — Why having the user computing the dual, when the main machinery (conic duality) is already implemented? Computing the conjugate of f may be easy, but deriving (2.5) may be not — tfocs_SCD requires that f be prox-capable, but f may be smooth and not prox-capable.

Because in fact, the machinery is not there. We do not compute general duals in TFOCS, only the very specific case of a prox-capable function plus the smoothing term.