# Representing the dual problem for a convex problem with expontential terms

The following problem has been proved to be a convex function by some transformation the details are in this paper Paper Download Convexity Proof

\min_{f_1,f_2} [\exp( \frac{d_1f_1}{\tau f_1 - d_1c_1}) -1] \frac{\tau f_1 - d_1c_1}{f_1} \exp(\frac{d_2f_2}{\tau f_2 - d_2c_2}) + [\exp( \frac{d_2f_2}{\tau f_2 - d_2c_2}) -1] \frac{\tau f_2 - d_2c_2}{f_2}
subject to
0< \exp( \frac{d_2f_2}{\tau f_2 - d_2c_2})[\exp(\frac{d_1f_1}{\tau f_1 - d_1c_1}) -1] \leq P
0< \exp( \frac{d_2f_2}{\tau f_2 - d_2c_2}) -1 \leq P
f_1 + f_2 \leq F
f_1 > 0 ,f_2 >0

my variables are f_1,f_2 and all other constants are positive. I want the right way to input the dual problem of this problem to the CVX.

The had a previous post to this problem Previous Post

The following problem has been proved to be a convex function by some transformation

What does that mean? Show us the transformation.

I uploaded the paper and the complete proof to the post. Thanks so much for your help.

There is not a DCP-compliant constructive proof of convexity, so you’re probably out of luck.

As for any dual program or dual decomposition, I think you’ll likely have to figure that out without any help from the forum. I have no idea what the dual looks like, or whether it is inputtable to CVX, but if you do, great. If that is spelled out in the paper or any references, I’ll let you dig it out.